0 00:00:00,000 --> 00:00:30,000 Dear viewer, these subtitles were generated by a machine via the service Trint and therefore are (very) buggy. If you are capable, please help us to create good quality subtitles: https://c3subtitles.de/talk/424 Thanks! 1 00:00:09,720 --> 00:00:12,119 OK, welcome to the Talk. 2 00:00:12,120 --> 00:00:13,589 If you're coming in, please close the 3 00:00:13,590 --> 00:00:14,590 door behind you, 4 00:00:16,590 --> 00:00:18,299 please give a warm applause to Mark knows 5 00:00:18,300 --> 00:00:19,529 he's going to talk about higher 6 00:00:19,530 --> 00:00:22,349 dimensional 40 geometry and fractals, 7 00:00:22,350 --> 00:00:24,869 which is he has an electric sheep and 8 00:00:24,870 --> 00:00:26,969 other exciting pictures. 9 00:00:35,200 --> 00:00:37,239 All right. Hello, everyone. 10 00:00:37,240 --> 00:00:39,669 Um, so this, 11 00:00:39,670 --> 00:00:41,979 as you might may have seen in 12 00:00:41,980 --> 00:00:43,389 the abstract, the stock will be split 13 00:00:43,390 --> 00:00:45,489 into three distinct sections. 14 00:00:45,490 --> 00:00:46,929 The thing about the topic is that it's 15 00:00:46,930 --> 00:00:47,769 extremely wide. 16 00:00:47,770 --> 00:00:49,899 I could probably feel a lecture for about 17 00:00:49,900 --> 00:00:51,639 a week, but we're not going to do that. 18 00:00:51,640 --> 00:00:53,949 So I 19 00:00:53,950 --> 00:00:55,899 am going to assume you roughly know how 20 00:00:55,900 --> 00:00:57,520 to do prospective predictors and predict 21 00:00:58,840 --> 00:01:00,489 if you do. And you might as well believe 22 00:01:00,490 --> 00:01:03,069 me, that that would be good, too. 23 00:01:03,070 --> 00:01:04,988 So for forty part, I'm going to I'm going 24 00:01:04,989 --> 00:01:07,519 to throw some formulas in there and 25 00:01:07,520 --> 00:01:08,520 how to do that. 26 00:01:09,610 --> 00:01:12,219 Then I'm going to talk about some 27 00:01:12,220 --> 00:01:13,779 information systems and how they 28 00:01:13,780 --> 00:01:14,949 generally work. 29 00:01:14,950 --> 00:01:17,079 And in particular, after 30 00:01:17,080 --> 00:01:18,219 that, I'm going to talk about fractal 31 00:01:18,220 --> 00:01:20,289 flames, which are a special kind of 32 00:01:20,290 --> 00:01:21,759 I try a different system. 33 00:01:21,760 --> 00:01:23,529 So the twist we're going to do here is 34 00:01:23,530 --> 00:01:25,689 that for a system and 35 00:01:25,690 --> 00:01:27,339 for effective flames, we're going to talk 36 00:01:27,340 --> 00:01:29,409 about how to do those in poverty 37 00:01:30,460 --> 00:01:31,329 now. 38 00:01:31,330 --> 00:01:33,609 And when I say 40 interdimensional, 39 00:01:33,610 --> 00:01:35,679 I mean, ah, to the power of 40 00:01:35,680 --> 00:01:36,819 four and higher. 41 00:01:36,820 --> 00:01:39,009 So it's not about higher 42 00:01:39,010 --> 00:01:41,559 dimensional stuff as you would have it in 43 00:01:41,560 --> 00:01:42,759 other fields of math. 44 00:01:42,760 --> 00:01:45,159 It's more it's more condensed 45 00:01:45,160 --> 00:01:46,809 into something specific. 46 00:01:46,810 --> 00:01:47,979 All right. And there's going to be some 47 00:01:47,980 --> 00:01:50,119 intermission slides where, uh, circa 48 00:01:50,120 --> 00:01:52,599 some demo program I got like the cheesy 49 00:01:52,600 --> 00:01:53,889 cereal possible. 50 00:01:53,890 --> 00:01:55,539 So you can follow that along in your 51 00:01:55,540 --> 00:01:57,469 browser if you feel like it. 52 00:01:57,470 --> 00:01:59,409 And let's get started. 53 00:01:59,410 --> 00:02:01,479 So when I said one 54 00:02:01,480 --> 00:02:03,669 at three parts, I am going to tell 55 00:02:03,670 --> 00:02:04,659 you what I'm skipping. 56 00:02:04,660 --> 00:02:06,729 So this is 57 00:02:06,730 --> 00:02:07,730 a cube. 58 00:02:08,440 --> 00:02:09,679 We've all seen a cube. 59 00:02:09,680 --> 00:02:12,099 Um, so 60 00:02:12,100 --> 00:02:13,479 this stuff I'm skipping because we don't 61 00:02:13,480 --> 00:02:15,699 have enough time is had 62 00:02:15,700 --> 00:02:17,919 to do the actual matrix American 63 00:02:17,920 --> 00:02:20,109 made products, which is like the 64 00:02:20,110 --> 00:02:21,819 basis for most of the linear algebra 65 00:02:21,820 --> 00:02:23,389 stuff you've heard of. 66 00:02:23,390 --> 00:02:25,929 I'm going to skip across product and 3D 67 00:02:25,930 --> 00:02:27,999 and I'm going to assume you're 68 00:02:28,000 --> 00:02:30,369 off. You know what in coordinates are 69 00:02:30,370 --> 00:02:32,589 if you don't, it's basically I don't no 70 00:02:32,590 --> 00:02:33,939 coordinate any hyperscale. 71 00:02:35,620 --> 00:02:36,849 I'm going to assume you trust me on 72 00:02:36,850 --> 00:02:39,039 rotations. You basically 73 00:02:39,040 --> 00:02:40,569 in three days you need a free cross-breed 74 00:02:40,570 --> 00:02:43,379 matrix to have a rotation. 75 00:02:43,380 --> 00:02:46,179 Um, there's going to 76 00:02:46,180 --> 00:02:47,679 be a reason for being organized. 77 00:02:47,680 --> 00:02:49,929 Cornets are that we want to have some 78 00:02:49,930 --> 00:02:51,369 fine transformations, which is basically 79 00:02:51,370 --> 00:02:53,559 the same. But we can also like translates 80 00:02:53,560 --> 00:02:56,079 of, uh, 81 00:02:56,080 --> 00:02:57,579 there's look at, uh, look at 82 00:02:57,580 --> 00:02:59,739 transformations in jail. 83 00:02:59,740 --> 00:03:01,509 So also skipping those. 84 00:03:01,510 --> 00:03:03,429 But we're going to extend them later. 85 00:03:03,430 --> 00:03:05,399 And there's something called perspective 86 00:03:05,400 --> 00:03:07,659 transform, which 87 00:03:07,660 --> 00:03:09,039 is. 88 00:03:09,040 --> 00:03:10,599 Yeah. Which is basically what we saw on 89 00:03:10,600 --> 00:03:13,389 the slide before, which it 90 00:03:13,390 --> 00:03:15,579 reduces the number of dimensions. 91 00:03:15,580 --> 00:03:17,439 So in Winfried case, you get a two day 92 00:03:17,440 --> 00:03:18,579 picture, which you can sort of your 93 00:03:18,580 --> 00:03:20,859 screen and. 94 00:03:20,860 --> 00:03:23,019 Well, yeah. So the perspective transform 95 00:03:23,020 --> 00:03:24,399 is something you do so you can learn to 96 00:03:24,400 --> 00:03:25,419 do predictions. 97 00:03:27,460 --> 00:03:28,659 There's going to be a lot of slides like 98 00:03:28,660 --> 00:03:29,569 this. 99 00:03:29,570 --> 00:03:32,349 Uh, so for example, 100 00:03:32,350 --> 00:03:34,599 I'm going to skip over it, but I'm not 101 00:03:34,600 --> 00:03:36,579 one of indentation like vectors in our 102 00:03:36,580 --> 00:03:38,709 stuff is going to are going to be bold, 103 00:03:38,710 --> 00:03:41,349 uh, vertical bars around the Matrix. 104 00:03:41,350 --> 00:03:43,269 I mean, that that we're going to do 105 00:03:43,270 --> 00:03:44,270 determinant. 106 00:03:45,370 --> 00:03:48,309 Uh, and 107 00:03:48,310 --> 00:03:50,499 when we have when we have rotation 108 00:03:50,500 --> 00:03:52,569 matrices, we can just extend 109 00:03:52,570 --> 00:03:54,819 them to be so you can multiply 110 00:03:54,820 --> 00:03:56,889 them with 111 00:03:56,890 --> 00:03:58,689 a fine transformation matrices. 112 00:03:58,690 --> 00:04:01,389 So you just add another row 113 00:04:01,390 --> 00:04:03,849 and you add another column, 114 00:04:03,850 --> 00:04:05,559 all zeros except for Lessel. 115 00:04:05,560 --> 00:04:07,809 So it's going to be interchangeable. 116 00:04:07,810 --> 00:04:09,909 So just just a heads up 117 00:04:09,910 --> 00:04:12,349 and this is a matrix we're also skipping. 118 00:04:12,350 --> 00:04:14,229 I'm just throwing that here because it 119 00:04:14,230 --> 00:04:15,519 looks kind of intimidating. 120 00:04:15,520 --> 00:04:17,648 It's documented in your own 121 00:04:17,649 --> 00:04:18,849 jail manual. So, 122 00:04:21,190 --> 00:04:23,439 yeah, just throwing 123 00:04:23,440 --> 00:04:24,509 it out there. 124 00:04:24,510 --> 00:04:26,889 OK, and 125 00:04:26,890 --> 00:04:28,509 Mexican-American anyway. 126 00:04:28,510 --> 00:04:31,779 So now part one, um, 127 00:04:31,780 --> 00:04:33,489 you guys are going to believe you can do 128 00:04:33,490 --> 00:04:36,039 prospecting for Texas and Freddy, 129 00:04:36,040 --> 00:04:37,479 probably because you've been playing golf 130 00:04:37,480 --> 00:04:39,009 duty or something at some point. 131 00:04:39,010 --> 00:04:41,139 So, so 132 00:04:41,140 --> 00:04:42,429 we can do that in 40. 133 00:04:42,430 --> 00:04:44,529 And this, for example, would be 134 00:04:44,530 --> 00:04:46,509 a tesseract or a hypercube. 135 00:04:46,510 --> 00:04:48,609 So in order to render this, we need 136 00:04:48,610 --> 00:04:51,069 to do some math to take our 40 137 00:04:51,070 --> 00:04:53,289 object, in this case, Tesseract, and 138 00:04:53,290 --> 00:04:55,509 reduce it to a 3D object, which we 139 00:04:55,510 --> 00:04:57,789 can then turn into a two 140 00:04:57,790 --> 00:04:59,139 object. 141 00:04:59,140 --> 00:05:00,939 And if we want to do it in five days, 142 00:05:00,940 --> 00:05:01,940 it's going to be the same thing. 143 00:05:04,390 --> 00:05:06,129 So again, what do we need for that? 144 00:05:06,130 --> 00:05:07,390 It's basically the same list 145 00:05:09,430 --> 00:05:10,430 shit. 146 00:05:12,910 --> 00:05:15,279 But and it gets worse because 147 00:05:15,280 --> 00:05:16,779 we don't actually have a cross product 148 00:05:16,780 --> 00:05:18,470 for the damnit. 149 00:05:19,780 --> 00:05:21,039 Well, we don't need a cross product. 150 00:05:21,040 --> 00:05:22,089 We just need normal's. 151 00:05:22,090 --> 00:05:23,849 And so I'm just going to do it different, 152 00:05:23,850 --> 00:05:24,850 which is a lot shorter. 153 00:05:26,140 --> 00:05:28,359 OK, so we want to do Normal's 154 00:05:28,360 --> 00:05:30,399 I was I was just showing him a slide from 155 00:05:30,400 --> 00:05:32,469 across product and it's pretty much the 156 00:05:32,470 --> 00:05:34,169 same, the same thing. 157 00:05:34,170 --> 00:05:36,269 But like in Fredi, 158 00:05:36,270 --> 00:05:38,099 we had a cross product and we take two 159 00:05:38,100 --> 00:05:40,409 vectors and we get an offer going 160 00:05:40,410 --> 00:05:41,579 back to that. 161 00:05:41,580 --> 00:05:44,309 So this is the property we we need 162 00:05:44,310 --> 00:05:45,629 to do a FedExes. 163 00:05:45,630 --> 00:05:47,789 Now, in 40, we can 164 00:05:47,790 --> 00:05:50,279 have two vectors and multiply 165 00:05:50,280 --> 00:05:51,419 them in some way to get something 166 00:05:51,420 --> 00:05:53,279 original. Because when we get a plane, 167 00:05:53,280 --> 00:05:55,529 because we didn't fix free 168 00:05:55,530 --> 00:05:57,720 of a vector, so we have one left over. 169 00:05:59,050 --> 00:06:02,309 Well, we can take three vectors and 170 00:06:02,310 --> 00:06:05,069 do the determinant with this matrix here, 171 00:06:05,070 --> 00:06:06,149 and that'll do it. 172 00:06:06,150 --> 00:06:08,159 So this gives us one of two vectors, just 173 00:06:08,160 --> 00:06:09,839 like we normally cross party. 174 00:06:09,840 --> 00:06:12,489 So we just solve the normal 175 00:06:12,490 --> 00:06:14,339 Grosberg problem. 176 00:06:14,340 --> 00:06:15,600 So, yeah, 177 00:06:17,280 --> 00:06:19,559 and of course we need no base vector 178 00:06:19,560 --> 00:06:21,029 because usually we just needed three of 179 00:06:21,030 --> 00:06:21,449 them. 180 00:06:21,450 --> 00:06:24,839 So I'm called I call this term because 181 00:06:24,840 --> 00:06:26,790 we all like quantum physics anyway. 182 00:06:29,850 --> 00:06:31,439 We can do this in higher dimensions. 183 00:06:31,440 --> 00:06:33,569 It basically looks the same, except we. 184 00:06:33,570 --> 00:06:36,059 So what we do is if we have 185 00:06:36,060 --> 00:06:38,789 anything in and we 186 00:06:38,790 --> 00:06:40,889 we need one less than that and then we 187 00:06:40,890 --> 00:06:43,079 can fix all the coronate and 188 00:06:43,080 --> 00:06:44,850 then we get a vector back, 189 00:06:46,020 --> 00:06:47,129 that's going to be your problem with 190 00:06:47,130 --> 00:06:49,949 that. So which is part of the 191 00:06:49,950 --> 00:06:51,420 formulas we need, we need later. 192 00:06:53,580 --> 00:06:55,889 I'm not gonna go into delve into 193 00:06:55,890 --> 00:06:58,049 the whole formulas and most of the time 194 00:06:58,050 --> 00:07:00,209 you can just read a read of and later I'm 195 00:07:00,210 --> 00:07:02,309 just going to figure out from version out 196 00:07:02,310 --> 00:07:04,049 that I use for this stuff. 197 00:07:04,050 --> 00:07:06,329 So, uh, another thing we need is a look 198 00:07:06,330 --> 00:07:08,249 at transformations in Fredi. 199 00:07:08,250 --> 00:07:10,589 I mean, you have like you have a point 200 00:07:10,590 --> 00:07:11,729 you're looking at and you have your 201 00:07:11,730 --> 00:07:13,919 camera, so you need to turn 202 00:07:13,920 --> 00:07:16,289 around and face that point. 203 00:07:16,290 --> 00:07:18,209 Fortunately, we don't actually need 204 00:07:18,210 --> 00:07:20,339 trigonometric functions because 205 00:07:20,340 --> 00:07:22,529 we can just, uh, we can 206 00:07:22,530 --> 00:07:25,799 just build a rotation matrix by 207 00:07:25,800 --> 00:07:28,109 filling in the last, uh, the last 208 00:07:28,110 --> 00:07:30,479 column of a matrix with, uh, 209 00:07:30,480 --> 00:07:31,769 what we're looking at minus where we're 210 00:07:31,770 --> 00:07:32,770 from. 211 00:07:33,120 --> 00:07:36,059 And then we need some orientation vectors 212 00:07:36,060 --> 00:07:38,249 and 40 we need two 213 00:07:38,250 --> 00:07:39,329 orientation vectors. 214 00:07:39,330 --> 00:07:41,159 If you're if you're looking at your 215 00:07:41,160 --> 00:07:43,259 Auburndale manual, you you have a 216 00:07:43,260 --> 00:07:45,239 function that does that for you. 217 00:07:45,240 --> 00:07:47,189 You get the three vectors, you give it 218 00:07:47,190 --> 00:07:48,569 where you're looking at, where you're 219 00:07:48,570 --> 00:07:50,679 looking from and which side is up. 220 00:07:50,680 --> 00:07:52,919 So because you could rotate the camera 221 00:07:52,920 --> 00:07:54,359 like this. 222 00:07:54,360 --> 00:07:56,689 So in 40, you need, 223 00:07:56,690 --> 00:07:58,679 uh, you need to fix another vector for 224 00:07:58,680 --> 00:07:59,009 that. 225 00:07:59,010 --> 00:08:01,649 So we have two from 226 00:08:01,650 --> 00:08:03,809 open back and we feel 227 00:08:03,810 --> 00:08:05,969 from right to left, we calculated 228 00:08:05,970 --> 00:08:08,039 the last column and 229 00:08:08,040 --> 00:08:10,199 we do our normal 230 00:08:10,200 --> 00:08:12,569 or cross product over, uh, 231 00:08:12,570 --> 00:08:13,769 of those vectors. 232 00:08:13,770 --> 00:08:16,229 And then we go to the left and we slide 233 00:08:16,230 --> 00:08:18,959 out one of the vectors 234 00:08:18,960 --> 00:08:20,159 and then we keep doing that. 235 00:08:20,160 --> 00:08:22,949 And the last one we have another normal 236 00:08:22,950 --> 00:08:25,109 for for for everything. 237 00:08:25,110 --> 00:08:27,389 Now, you can actually find this in 238 00:08:27,390 --> 00:08:29,459 some publications online, but you 239 00:08:29,460 --> 00:08:30,509 can't find this, 240 00:08:31,620 --> 00:08:32,548 which is what we do. 241 00:08:32,549 --> 00:08:34,439 And we want to do it in like days and 242 00:08:34,440 --> 00:08:35,038 stuff. 243 00:08:35,039 --> 00:08:36,389 It still looks the same, 244 00:08:37,470 --> 00:08:38,470 but it's ugly. 245 00:08:39,659 --> 00:08:42,178 But, uh, basically we still have 246 00:08:42,179 --> 00:08:43,678 we have to lessen the number of 247 00:08:43,679 --> 00:08:45,749 dimensions. And then we, uh, we 248 00:08:45,750 --> 00:08:47,159 slide. 249 00:08:47,160 --> 00:08:48,160 We slide. 250 00:08:49,410 --> 00:08:51,569 We slightly calculated columns 251 00:08:51,570 --> 00:08:53,609 in from the right and calculate towards 252 00:08:53,610 --> 00:08:54,610 the left. 253 00:08:55,650 --> 00:08:56,549 Right. 254 00:08:56,550 --> 00:08:58,079 So we also want to do a prospective 255 00:08:58,080 --> 00:09:00,779 transformation, which is what 256 00:09:00,780 --> 00:09:02,590 basically, um, 257 00:09:03,660 --> 00:09:05,129 basically you have a camera like this 258 00:09:05,130 --> 00:09:06,209 instead of like this. 259 00:09:06,210 --> 00:09:07,889 So it goes like two sides. 260 00:09:07,890 --> 00:09:10,229 So that's part of the respective thing. 261 00:09:10,230 --> 00:09:12,319 Fortunately, since 262 00:09:12,320 --> 00:09:13,799 Auburndale is actually taking care of all 263 00:09:13,800 --> 00:09:15,749 the cut offs and everything, and we we 264 00:09:15,750 --> 00:09:17,879 just want to free the object, we can skip 265 00:09:17,880 --> 00:09:20,099 a lot of stuff. And The Matrix doesn't 266 00:09:20,100 --> 00:09:22,919 look nearly as our base of predicates. 267 00:09:22,920 --> 00:09:25,019 So we can use a simple 268 00:09:25,020 --> 00:09:26,129 matrix like this. 269 00:09:26,130 --> 00:09:28,199 What we want to do is we only 270 00:09:28,200 --> 00:09:29,200 have a triangle 271 00:09:30,360 --> 00:09:32,489 which is like how wide our 272 00:09:32,490 --> 00:09:34,649 I can look and everything. 273 00:09:34,650 --> 00:09:36,809 But the last but the last two 274 00:09:36,810 --> 00:09:39,149 dimensions, I mean the last one 275 00:09:39,150 --> 00:09:42,059 dimension and this is V homogenous part, 276 00:09:42,060 --> 00:09:43,859 they're fixed with the eye angle. 277 00:09:43,860 --> 00:09:46,379 So the last coordinate 278 00:09:46,380 --> 00:09:48,959 in our forty five fifty whatever 279 00:09:48,960 --> 00:09:50,399 is always kind of like a death. 280 00:09:51,600 --> 00:09:53,669 So yeah. 281 00:09:53,670 --> 00:09:55,049 So basically that works. 282 00:09:55,050 --> 00:09:57,779 The five decades is pretty much trivial. 283 00:09:57,780 --> 00:10:00,059 We just have the last two fixed and 284 00:10:00,060 --> 00:10:02,279 whatever we have is uh corrected 285 00:10:02,280 --> 00:10:03,809 with the angle formula we had in 286 00:10:03,810 --> 00:10:04,810 affricate. 287 00:10:05,550 --> 00:10:07,289 So that takes care of that. 288 00:10:08,340 --> 00:10:10,469 And then we need some kind of 289 00:10:10,470 --> 00:10:12,299 matrix which is basically like we take 290 00:10:12,300 --> 00:10:14,549 all of this stuff, put it all together, 291 00:10:14,550 --> 00:10:16,139 and then we're happy because we only have 292 00:10:16,140 --> 00:10:17,969 one matrix that we have to multiply away 293 00:10:17,970 --> 00:10:18,970 for a vector. 294 00:10:19,650 --> 00:10:21,839 And it's not that that is just a couple 295 00:10:21,840 --> 00:10:23,469 of matrix multiplications. 296 00:10:23,470 --> 00:10:25,439 This is actually a focus for Matrix. 297 00:10:25,440 --> 00:10:27,599 And this is the five and this is a five 298 00:10:27,600 --> 00:10:29,189 plus five. 299 00:10:29,190 --> 00:10:31,889 But that's not so bad because we can just 300 00:10:31,890 --> 00:10:33,939 so we implicitly expand this one to five. 301 00:10:33,940 --> 00:10:36,009 S5 with, as 302 00:10:36,010 --> 00:10:38,079 I previously explained, so 303 00:10:38,080 --> 00:10:40,189 not to that four and the five decades 304 00:10:40,190 --> 00:10:41,799 is pretty much pretty much the same. 305 00:10:41,800 --> 00:10:43,059 So we don't really have to worry about 306 00:10:43,060 --> 00:10:45,190 this. So I mean, five D and higher. 307 00:10:46,210 --> 00:10:48,429 So what 308 00:10:48,430 --> 00:10:50,529 do we do once we did our 309 00:10:50,530 --> 00:10:53,469 matrix vector matrix multiplication? 310 00:10:53,470 --> 00:10:56,289 So we still need to actually convert. 311 00:10:56,290 --> 00:10:58,509 So we gave it a homogenous 40 312 00:10:58,510 --> 00:11:00,849 coronate and our matrix 313 00:11:00,850 --> 00:11:03,429 and we multiply those and 314 00:11:03,430 --> 00:11:06,339 then we get a still a five coordinate 315 00:11:06,340 --> 00:11:07,340 back. 316 00:11:09,010 --> 00:11:10,330 And at this point 317 00:11:12,730 --> 00:11:14,649 we need to take me home locking this part 318 00:11:14,650 --> 00:11:15,039 out. 319 00:11:15,040 --> 00:11:17,679 And we also need to do a prospective 320 00:11:17,680 --> 00:11:18,609 division. 321 00:11:18,610 --> 00:11:20,109 So this is the same function in both 322 00:11:20,110 --> 00:11:22,599 cases. So we just apply that twice and 323 00:11:22,600 --> 00:11:23,859 then we get free director back 324 00:11:25,000 --> 00:11:26,679 and that's basically it. 325 00:11:26,680 --> 00:11:28,569 So now we have a 3D vector. 326 00:11:28,570 --> 00:11:29,709 We do the 3D thing again. 327 00:11:29,710 --> 00:11:31,749 We have cameras for every dimension and 328 00:11:31,750 --> 00:11:33,069 we're going. 329 00:11:33,070 --> 00:11:34,119 So, yeah, 330 00:11:35,260 --> 00:11:37,389 and I just show how that is done 331 00:11:38,680 --> 00:11:39,729 or at least what it looks like. 332 00:11:39,730 --> 00:11:41,259 So this is we have a clip from here 333 00:11:42,670 --> 00:11:44,919 and we can rotate 334 00:11:44,920 --> 00:11:47,169 this and pretty nothing too fancy. 335 00:11:48,610 --> 00:11:50,499 A little program I wrote a while back 336 00:11:51,550 --> 00:11:52,820 and we can do it in 40. 337 00:11:54,220 --> 00:11:55,690 So it turns inside out 338 00:11:56,740 --> 00:11:59,469 yay terms and set up. 339 00:11:59,470 --> 00:12:01,869 If we did this with a 3D 340 00:12:01,870 --> 00:12:04,089 thing and 40, 341 00:12:04,090 --> 00:12:06,339 we would basically turn the whole thing 342 00:12:06,340 --> 00:12:08,619 inside out because we do a 40 rotation 343 00:12:08,620 --> 00:12:10,719 Afridi's object and 344 00:12:10,720 --> 00:12:12,179 we can also do this in 50. 345 00:12:14,970 --> 00:12:17,069 And I think it 346 00:12:17,070 --> 00:12:19,140 gets kind of confusing after five, it's. 347 00:12:24,210 --> 00:12:25,440 The rest of it for. 348 00:12:26,550 --> 00:12:27,550 Seiner. 349 00:12:28,770 --> 00:12:29,770 All right. 350 00:12:31,680 --> 00:12:34,229 OK, now I promise 351 00:12:34,230 --> 00:12:36,209 I'll read it from some systems, we're 352 00:12:36,210 --> 00:12:37,589 going to have to skip over a couple of 353 00:12:37,590 --> 00:12:39,329 these things so it's not too bad. 354 00:12:39,330 --> 00:12:40,949 So, Nightrider, folks, this is the basic 355 00:12:40,950 --> 00:12:43,169 idea is that you have you have like 356 00:12:43,170 --> 00:12:45,299 two free four functions and you 357 00:12:45,300 --> 00:12:47,609 have a set of starting vectors. 358 00:12:47,610 --> 00:12:49,709 So you multiply 359 00:12:49,710 --> 00:12:52,019 all of these with all of them and 360 00:12:52,020 --> 00:12:53,729 they do that recursively and they 361 00:12:53,730 --> 00:12:55,799 function like this and sum it all up. 362 00:12:55,800 --> 00:12:58,199 And this is actually from a fractal flame 363 00:12:58,200 --> 00:12:59,369 paper. 364 00:12:59,370 --> 00:13:00,869 I don't quite agree with that because we 365 00:13:00,870 --> 00:13:02,879 don't we don't really do that ad 366 00:13:02,880 --> 00:13:05,189 infinitum when we destroy it, 367 00:13:05,190 --> 00:13:07,199 because then we wouldn't see anything 368 00:13:07,200 --> 00:13:08,429 because it would never stop. 369 00:13:08,430 --> 00:13:10,859 So that. Yeah, but that's what the 370 00:13:10,860 --> 00:13:12,569 effect of flame paper had. 371 00:13:12,570 --> 00:13:14,729 So we can basically 372 00:13:14,730 --> 00:13:16,109 choose any kind of function we want for 373 00:13:16,110 --> 00:13:17,359 this. 374 00:13:17,360 --> 00:13:18,600 A simple one is we 375 00:13:20,250 --> 00:13:21,570 are fine transformation's, 376 00:13:22,680 --> 00:13:24,809 which are basically we can we can 377 00:13:24,810 --> 00:13:26,879 like take your point, we can 378 00:13:26,880 --> 00:13:28,710 translate it and we can rotate it. 379 00:13:29,890 --> 00:13:32,249 So normally you Dukas 380 00:13:32,250 --> 00:13:34,559 game to render these things, which is 381 00:13:34,560 --> 00:13:35,969 which is explain later. 382 00:13:35,970 --> 00:13:37,439 But I'm not going to do that because we 383 00:13:37,440 --> 00:13:39,599 can't it doesn't 384 00:13:39,600 --> 00:13:42,029 work in 40 or Fredi because 385 00:13:42,030 --> 00:13:42,989 you need too many points. 386 00:13:42,990 --> 00:13:45,659 So what we can do is we take a 387 00:13:45,660 --> 00:13:48,059 sufficiently divided, primitive 388 00:13:48,060 --> 00:13:49,439 and then apply all of these functions 389 00:13:49,440 --> 00:13:50,759 recursively and then we get pretty 390 00:13:50,760 --> 00:13:51,760 pictures. 391 00:13:54,210 --> 00:13:55,979 So, for example, if we tried to do a 392 00:13:55,980 --> 00:13:58,229 Stravinsky gasket, we have this 393 00:13:58,230 --> 00:14:00,509 square and then we can 394 00:14:00,510 --> 00:14:01,529 we have free functions. 395 00:14:01,530 --> 00:14:03,719 And they were like this where we go 396 00:14:03,720 --> 00:14:05,909 on it and then make it smaller, which 397 00:14:05,910 --> 00:14:07,469 we can all do with fine transformations. 398 00:14:07,470 --> 00:14:09,329 We do that a couple of times recursively 399 00:14:09,330 --> 00:14:11,129 and we can never, ever nicer, never 400 00:14:11,130 --> 00:14:12,130 sharper picture. 401 00:14:13,830 --> 00:14:16,739 So does this work and pretty enough? 402 00:14:16,740 --> 00:14:17,740 Sure. 403 00:14:18,810 --> 00:14:19,810 Uh. 404 00:14:21,090 --> 00:14:21,989 We can't do that. 405 00:14:21,990 --> 00:14:22,990 There's no problem here. 406 00:14:25,020 --> 00:14:27,689 I'm going to stick with a pretty one, 407 00:14:27,690 --> 00:14:30,279 these are randomly generated just 408 00:14:30,280 --> 00:14:32,699 with the seeds. So it's just, you know, 409 00:14:32,700 --> 00:14:34,259 so nothing too fancy here. 410 00:14:34,260 --> 00:14:35,159 We converted this. 411 00:14:35,160 --> 00:14:36,160 It looks pretty. 412 00:14:37,100 --> 00:14:39,179 You can do this in 40 and turn 413 00:14:39,180 --> 00:14:40,180 it inside out. 414 00:14:43,610 --> 00:14:46,399 And so 415 00:14:46,400 --> 00:14:48,109 you can turn it inside out, as you see 416 00:14:48,110 --> 00:14:50,419 here, sort of, 417 00:14:50,420 --> 00:14:52,479 well, some systems in too deep, 418 00:14:52,480 --> 00:14:53,779 but they use a special kind of function 419 00:14:53,780 --> 00:14:55,969 called a variation, which is 420 00:14:55,970 --> 00:14:58,089 defined in that fructify 421 00:14:58,090 --> 00:15:00,259 paper by Scott Scottrade, which 422 00:15:00,260 --> 00:15:02,119 is reference NBA. And so you can read it 423 00:15:02,120 --> 00:15:03,120 because it's cool. 424 00:15:04,490 --> 00:15:06,529 And the variations kind of work like 425 00:15:06,530 --> 00:15:08,809 this, you have your afine transformation 426 00:15:08,810 --> 00:15:11,089 and you also apply 427 00:15:11,090 --> 00:15:13,249 a set of their 428 00:15:13,250 --> 00:15:15,379 variation. Functions which are 429 00:15:15,380 --> 00:15:16,789 defined in appendix was like 40 430 00:15:16,790 --> 00:15:17,790 noncanonical ones. 431 00:15:19,310 --> 00:15:20,809 They kind of look like this. 432 00:15:20,810 --> 00:15:22,939 So, for example, we 433 00:15:22,940 --> 00:15:25,069 can have a function that does not think 434 00:15:25,070 --> 00:15:27,739 we can have some smet apply signs to 435 00:15:27,740 --> 00:15:29,449 to all of the coordinates 436 00:15:31,040 --> 00:15:33,319 and also like an almost 437 00:15:33,320 --> 00:15:35,449 Feargal transform all sorts 438 00:15:35,450 --> 00:15:37,129 of kind of funky things. 439 00:15:37,130 --> 00:15:40,239 There's a couple of weird concerns and 440 00:15:40,240 --> 00:15:42,079 they thought about some cool stuff there. 441 00:15:42,080 --> 00:15:44,239 So what you do is you you 442 00:15:44,240 --> 00:15:47,269 take a number of these variations 443 00:15:47,270 --> 00:15:48,949 and then you blend him together by 444 00:15:48,950 --> 00:15:51,049 assigning weights for each of the 445 00:15:51,050 --> 00:15:53,209 variations you want and adding 446 00:15:53,210 --> 00:15:55,279 it all together so you can 447 00:15:55,280 --> 00:15:58,099 have like half of a spherical one 448 00:15:58,100 --> 00:16:00,449 quarter of a linear one and 449 00:16:00,450 --> 00:16:02,629 another quarter 450 00:16:02,630 --> 00:16:03,919 of the cosine one. 451 00:16:03,920 --> 00:16:05,599 You can also make it more than one, but 452 00:16:05,600 --> 00:16:06,600 then it kind of looks weird. 453 00:16:08,330 --> 00:16:10,399 So then you can also 454 00:16:10,400 --> 00:16:12,259 then they also added post transforms with 455 00:16:12,260 --> 00:16:14,059 this, which is you take another one of 456 00:16:14,060 --> 00:16:16,279 these and do it again and a final 457 00:16:16,280 --> 00:16:17,299 one. 458 00:16:17,300 --> 00:16:19,429 Yeah, they they really like that 459 00:16:19,430 --> 00:16:21,589 transfer as they do it everywhere, which 460 00:16:21,590 --> 00:16:22,429 is kind of cool. 461 00:16:22,430 --> 00:16:24,409 So when I said 462 00:16:25,720 --> 00:16:27,499 the things that Mackerras gave earlier, 463 00:16:27,500 --> 00:16:29,569 so if you only do the Keres 464 00:16:29,570 --> 00:16:31,069 game that's normal described, you get a 465 00:16:31,070 --> 00:16:33,199 black and white picture, some 466 00:16:33,200 --> 00:16:35,389 pixels are hit, some aren't. 467 00:16:35,390 --> 00:16:37,100 That's not really pretty. 468 00:16:38,600 --> 00:16:40,939 You can improve that by counting 469 00:16:40,940 --> 00:16:42,439 the number of times you hit a particular 470 00:16:42,440 --> 00:16:44,629 pixel and you have a grayscale image, 471 00:16:44,630 --> 00:16:46,369 which is better. 472 00:16:46,370 --> 00:16:48,469 It's a lot better if you take longer 473 00:16:48,470 --> 00:16:50,629 to do that because you have lots of spots 474 00:16:50,630 --> 00:16:52,579 that get hit. A lot of times, lots of 475 00:16:52,580 --> 00:16:53,779 randomness in there. 476 00:16:53,780 --> 00:16:55,879 So you want to smooth out some 477 00:16:55,880 --> 00:16:57,649 of these smaller things. 478 00:16:57,650 --> 00:16:59,779 So small differences, but you 479 00:16:59,780 --> 00:17:01,009 still want to show like some of the 480 00:17:01,010 --> 00:17:03,109 bigger ones. So it kind of worked 481 00:17:03,110 --> 00:17:04,249 for them. 482 00:17:04,250 --> 00:17:07,219 And if you like a column that 483 00:17:07,220 --> 00:17:08,929 the way they do that is like every 484 00:17:08,930 --> 00:17:10,549 function you have because you still have 485 00:17:10,550 --> 00:17:11,659 more than one function. 486 00:17:11,660 --> 00:17:13,848 Every function gets an index on a color 487 00:17:13,849 --> 00:17:16,879 map and you mix them all together 488 00:17:16,880 --> 00:17:18,889 and then you get much prettier pictures 489 00:17:18,890 --> 00:17:19,939 and then you add some 490 00:17:20,960 --> 00:17:23,269 vibrancy algorithm. 491 00:17:23,270 --> 00:17:24,270 Always good. 492 00:17:25,790 --> 00:17:27,919 Now, as 493 00:17:27,920 --> 00:17:29,569 I said this, everything is strictly in 494 00:17:29,570 --> 00:17:31,669 2D, so 495 00:17:31,670 --> 00:17:33,980 it looks pretty, but it's not. 496 00:17:35,670 --> 00:17:37,259 So can we do that in 3-D? 497 00:17:37,260 --> 00:17:39,119 Well, we can't do if the can't because we 498 00:17:39,120 --> 00:17:40,469 don't have enough memory for that, 499 00:17:41,760 --> 00:17:43,499 but we can do it. 500 00:17:45,690 --> 00:17:47,539 We can do it with a discrete version. 501 00:17:52,200 --> 00:17:53,200 So, 502 00:17:54,990 --> 00:17:56,819 yeah, it's been some fun time on this on 503 00:17:56,820 --> 00:17:57,980 this program stuff, 504 00:17:59,640 --> 00:18:01,859 so it doesn't crash, 505 00:18:03,730 --> 00:18:05,999 OK, so 506 00:18:07,210 --> 00:18:08,639 we want more possession. 507 00:18:08,640 --> 00:18:10,159 We want this to be bigger. 508 00:18:10,160 --> 00:18:11,799 It's already kind of looks cool. 509 00:18:11,800 --> 00:18:13,229 It's already in 40. 510 00:18:13,230 --> 00:18:14,669 So let's stick with her three decades 511 00:18:14,670 --> 00:18:15,670 from now. 512 00:18:19,200 --> 00:18:20,579 You still get the effect of it turning 513 00:18:20,580 --> 00:18:22,649 inside out and everything, so it's kind 514 00:18:22,650 --> 00:18:24,659 of a random one, just the first best seat 515 00:18:24,660 --> 00:18:25,660 I had. 516 00:18:26,610 --> 00:18:28,199 You notice that it's too deep because I 517 00:18:28,200 --> 00:18:30,450 just took a plane and subdivided it. 518 00:18:31,890 --> 00:18:33,209 A lot of times. 519 00:18:33,210 --> 00:18:35,879 And then you run the 520 00:18:35,880 --> 00:18:37,859 transforms, you can sort of extend some 521 00:18:37,860 --> 00:18:40,109 of them, like I've seen the cosine one. 522 00:18:40,110 --> 00:18:41,609 And you can just add a number of cosine. 523 00:18:41,610 --> 00:18:42,659 You've seen this very good one. 524 00:18:42,660 --> 00:18:44,249 You have a formula for Steer's narrative. 525 00:18:44,250 --> 00:18:45,179 And so all this. 526 00:18:45,180 --> 00:18:47,279 Well, and we can do 527 00:18:47,280 --> 00:18:48,280 that. 528 00:18:49,050 --> 00:18:51,539 We can't do it. Do that in 40 also, 529 00:18:51,540 --> 00:18:53,609 which means our stuff can turn it inside 530 00:18:53,610 --> 00:18:56,009 out. The cool part of an effective flame 531 00:18:56,010 --> 00:18:57,839 is actually the way the colors work, 532 00:19:00,030 --> 00:19:02,069 which turns out is really, really easy to 533 00:19:02,070 --> 00:19:04,379 implement in a in a pixel shader. 534 00:19:04,380 --> 00:19:06,029 If you're willing to do a logarithm and a 535 00:19:06,030 --> 00:19:07,030 pixel shader 536 00:19:08,430 --> 00:19:10,199 sounds worse than it is, it actually 537 00:19:10,200 --> 00:19:11,849 works pretty well in real time. 538 00:19:11,850 --> 00:19:14,249 So this is rendered in real time. 539 00:19:14,250 --> 00:19:17,129 It's not the prettiest said ever, 540 00:19:17,130 --> 00:19:18,449 but there's some room for improvement 541 00:19:18,450 --> 00:19:19,450 here. So 542 00:19:20,610 --> 00:19:23,129 and it's kind of nice to see that, 543 00:19:23,130 --> 00:19:25,409 that it's still pretty damn smooth 544 00:19:25,410 --> 00:19:27,809 so I can do some random colors. 545 00:19:28,840 --> 00:19:30,359 OK, let's take this one. 546 00:19:30,360 --> 00:19:32,909 So like the yellow and the 547 00:19:32,910 --> 00:19:35,099 purple and the blue, which 548 00:19:35,100 --> 00:19:36,569 is sort of visible, there are all 549 00:19:36,570 --> 00:19:37,949 different functions and they get mixed 550 00:19:37,950 --> 00:19:39,899 together in the pixel shader, which works 551 00:19:39,900 --> 00:19:40,940 surprisingly well 552 00:19:43,560 --> 00:19:45,929 and can do all sorts 553 00:19:45,930 --> 00:19:46,930 of pretty well and. 554 00:19:50,290 --> 00:19:52,119 Four years on, it's actually pretty nice 555 00:19:52,120 --> 00:19:54,519 because it highlights 556 00:19:54,520 --> 00:19:55,520 some of the properties. 557 00:19:56,710 --> 00:19:58,089 This one is pretty good. 558 00:19:58,090 --> 00:20:00,229 So depending on from where we look, 559 00:20:00,230 --> 00:20:01,859 our pics of Qader with your original 560 00:20:01,860 --> 00:20:04,109 Ibram has this kind of property of 561 00:20:04,110 --> 00:20:05,949 amplifying geometry, which is pretty 562 00:20:05,950 --> 00:20:08,079 cool. And we can again do this 563 00:20:08,080 --> 00:20:10,209 in any kind of mention we want. 564 00:20:10,210 --> 00:20:13,899 So we have this cool thing and 565 00:20:13,900 --> 00:20:15,640 we can make it turn inside out. 566 00:20:17,850 --> 00:20:19,400 Well, sorta. 567 00:20:22,070 --> 00:20:23,029 Right. 568 00:20:23,030 --> 00:20:25,339 So you get this nebula 569 00:20:25,340 --> 00:20:27,919 and by doing a 40, 40 570 00:20:27,920 --> 00:20:30,109 insideout thing, you can 571 00:20:30,110 --> 00:20:32,239 make some pretty amazing pictures 572 00:20:32,240 --> 00:20:33,499 if you find that kind of seeing 573 00:20:33,500 --> 00:20:34,459 everything. 574 00:20:34,460 --> 00:20:37,009 So this thing, 575 00:20:37,010 --> 00:20:40,339 this piece of code is all 576 00:20:40,340 --> 00:20:41,340 open source. 577 00:20:42,320 --> 00:20:45,199 It's all all available on on GitHub. 578 00:20:45,200 --> 00:20:46,729 You can play with it every once in your 579 00:20:46,730 --> 00:20:48,919 browser, although unfortunately, 580 00:20:48,920 --> 00:20:50,209 it turns out that Web T.L. 581 00:20:50,210 --> 00:20:51,210 doesn't support 582 00:20:52,370 --> 00:20:54,439 doesn't seem to support 583 00:20:54,440 --> 00:20:56,419 this floating point texture's. 584 00:20:56,420 --> 00:20:58,489 We just need to cound ones 585 00:20:58,490 --> 00:21:00,539 up, unfortunately, Vavasour clan. 586 00:21:00,540 --> 00:21:02,029 So it doesn't really work, which is kind 587 00:21:02,030 --> 00:21:04,219 of sad, but we can, 588 00:21:04,220 --> 00:21:06,319 but it still works in principle and you 589 00:21:06,320 --> 00:21:08,389 can play it with most of the most of the 590 00:21:08,390 --> 00:21:10,340 other things. Um, so yeah. 591 00:21:11,540 --> 00:21:13,519 Uh, that's a program if you're 592 00:21:13,520 --> 00:21:15,139 interested. There's a block series 593 00:21:15,140 --> 00:21:17,179 explaining most of the formulas more in 594 00:21:17,180 --> 00:21:19,459 more detail because it just wouldn't cut 595 00:21:19,460 --> 00:21:20,460 it. 596 00:21:21,020 --> 00:21:23,839 Uh, this is my, uh, Twitter, 597 00:21:23,840 --> 00:21:25,189 if you're interested. 598 00:21:25,190 --> 00:21:27,079 Here's your original paper about the fact 599 00:21:27,080 --> 00:21:28,909 of Flamini written by Scott Race and 600 00:21:28,910 --> 00:21:31,309 Every Corexit, which is a really amazing 601 00:21:31,310 --> 00:21:32,989 read. And they put a lot of cool stuff in 602 00:21:32,990 --> 00:21:35,209 there. So I always give it a read. 603 00:21:35,210 --> 00:21:37,369 And as I said, something 604 00:21:37,370 --> 00:21:38,660 much more French 605 00:21:39,980 --> 00:21:41,629 we've all seen I'll see one. 606 00:21:41,630 --> 00:21:42,929 And that's the end of that one. 607 00:21:42,930 --> 00:21:44,330 So if anyone has any questions. 608 00:21:56,730 --> 00:21:59,069 OK, thank you, Magnum, for this really 609 00:21:59,070 --> 00:22:01,349 interesting talk. I really, really liked 610 00:22:01,350 --> 00:22:03,479 fractals. I'm sure everybody here does 611 00:22:03,480 --> 00:22:04,589 as well. 612 00:22:04,590 --> 00:22:06,479 Before we start with questions, if you 613 00:22:06,480 --> 00:22:08,579 absolutely have to leave, please be 614 00:22:08,580 --> 00:22:10,530 quiet. That involves no talking. 615 00:22:12,270 --> 00:22:13,799 If you can, please just stay until the 616 00:22:13,800 --> 00:22:16,409 end of questions. 617 00:22:16,410 --> 00:22:18,629 So are there any 618 00:22:18,630 --> 00:22:20,999 questions from the Internet signal 619 00:22:21,000 --> 00:22:22,000 angel? 620 00:22:23,290 --> 00:22:24,789 Can you wave at me if you have any 621 00:22:24,790 --> 00:22:26,079 questions? 622 00:22:26,080 --> 00:22:27,080 Is there a question? 623 00:22:28,020 --> 00:22:29,609 Yes, OK. 624 00:22:29,610 --> 00:22:30,610 Ask away. 625 00:22:37,970 --> 00:22:40,369 All the angels or so, 626 00:22:40,370 --> 00:22:41,899 could you please turn on the second 627 00:22:41,900 --> 00:22:42,900 largest microphone? 628 00:22:46,330 --> 00:22:47,979 Maybe start. Let's start with a question 629 00:22:47,980 --> 00:22:50,259 from microphone number three until 630 00:22:50,260 --> 00:22:51,789 the signal is just set up. 631 00:22:51,790 --> 00:22:54,639 Hey, thank you for your interest in, um, 632 00:22:54,640 --> 00:22:57,579 I was wondering, in the production, 633 00:22:57,580 --> 00:22:59,799 uh, transformation that you explain, you 634 00:22:59,800 --> 00:23:02,469 assume that the last 635 00:23:02,470 --> 00:23:03,849 dimension, it's one. 636 00:23:03,850 --> 00:23:06,189 So it's going to be depth 637 00:23:06,190 --> 00:23:08,409 and then you you you 638 00:23:08,410 --> 00:23:09,849 assume that the rest are going to 639 00:23:09,850 --> 00:23:10,749 collapse. 640 00:23:10,750 --> 00:23:12,909 Uh, my question is, what happens if you 641 00:23:12,910 --> 00:23:14,979 don't assume that or if there is 642 00:23:14,980 --> 00:23:16,989 anything that changes? 643 00:23:16,990 --> 00:23:19,089 Because in the in the 644 00:23:19,090 --> 00:23:21,249 projection, you're kind of assuming 645 00:23:21,250 --> 00:23:24,249 how the prediction is done to 3-D. 646 00:23:24,250 --> 00:23:25,179 Right. 647 00:23:25,180 --> 00:23:27,159 If I understand correctly that that is 648 00:23:27,160 --> 00:23:28,989 true, I haven't actually explored what 649 00:23:28,990 --> 00:23:30,939 happens if we do a different kind of 3D 650 00:23:30,940 --> 00:23:33,039 transform in in this case. 651 00:23:33,040 --> 00:23:34,040 So, 652 00:23:35,590 --> 00:23:36,819 I mean, this perceptually could be 653 00:23:36,820 --> 00:23:37,569 different. 654 00:23:37,570 --> 00:23:38,889 It could be. 655 00:23:38,890 --> 00:23:41,049 I've just tried to take the 656 00:23:41,050 --> 00:23:43,059 prospective projection as you see the and 657 00:23:43,060 --> 00:23:45,289 extend it to to 14, 14, 15 658 00:23:45,290 --> 00:23:47,469 higher. So I'm an expert if it gets 659 00:23:47,470 --> 00:23:49,269 different, but it would definitely be 660 00:23:49,270 --> 00:23:50,649 amazing to try that out. 661 00:23:50,650 --> 00:23:52,269 So I totally agree. 662 00:23:52,270 --> 00:23:53,270 Yeah. 663 00:23:54,250 --> 00:23:55,569 OK, single angel, do you have a 664 00:23:55,570 --> 00:23:56,559 microphone. 665 00:23:56,560 --> 00:23:57,339 Yes I have. 666 00:23:57,340 --> 00:23:59,679 OK, please ask away standard user 667 00:23:59,680 --> 00:24:02,649 from ISC asks are these visualization 668 00:24:02,650 --> 00:24:04,869 applicable to the 3D virtual 669 00:24:04,870 --> 00:24:06,999 reality experience and 670 00:24:07,000 --> 00:24:09,279 will that give us the ability to better 671 00:24:09,280 --> 00:24:11,209 understand one of the 672 00:24:12,460 --> 00:24:13,569 fractals and project? 673 00:24:13,570 --> 00:24:15,819 Since I'm I'm sure 674 00:24:15,820 --> 00:24:18,159 that if we have um, 675 00:24:18,160 --> 00:24:20,589 if we have something, a virtual reality 676 00:24:20,590 --> 00:24:22,899 answer that can that can 677 00:24:22,900 --> 00:24:25,089 do things in 3D right in front of us, 678 00:24:25,090 --> 00:24:27,399 that would completely, 679 00:24:27,400 --> 00:24:29,259 completely improve the experience and it 680 00:24:29,260 --> 00:24:31,119 would definitely help us explore behere 681 00:24:31,120 --> 00:24:32,289 dimensions better. 682 00:24:32,290 --> 00:24:34,359 So I have again 683 00:24:34,360 --> 00:24:35,439 tried it. 684 00:24:35,440 --> 00:24:37,329 But if someone would like to try that 685 00:24:37,330 --> 00:24:39,669 with VR, dear, the first 686 00:24:39,670 --> 00:24:40,670 test it. 687 00:24:43,180 --> 00:24:45,369 OK, let's go back to microphone number 688 00:24:45,370 --> 00:24:46,899 three, please. 689 00:24:46,900 --> 00:24:48,639 Yeah, just a quick question. 690 00:24:48,640 --> 00:24:50,169 I noticed that even for the 691 00:24:50,170 --> 00:24:51,969 multidimensional cases you used, 692 00:24:51,970 --> 00:24:54,519 apparently to the primitives as the 693 00:24:54,520 --> 00:24:55,520 primitive sea. 694 00:24:56,300 --> 00:24:57,849 Would it be possible to use the high 695 00:24:57,850 --> 00:24:59,319 dimensional primitives? 696 00:24:59,320 --> 00:25:01,069 It would definitely be possible. 697 00:25:01,070 --> 00:25:03,249 So, as you said, what I did 698 00:25:03,250 --> 00:25:04,420 was I still use tries 699 00:25:06,250 --> 00:25:08,439 and I kind of cheated by basically making 700 00:25:08,440 --> 00:25:10,599 them see fruit as in because if you had 701 00:25:10,600 --> 00:25:12,699 a 40, if you're looking 702 00:25:12,700 --> 00:25:14,919 at a 3D object with 40, you can see 703 00:25:14,920 --> 00:25:17,019 all the all facets simultaneously. 704 00:25:17,020 --> 00:25:19,269 So it would definitely 705 00:25:19,270 --> 00:25:21,579 be possible to to take 706 00:25:21,580 --> 00:25:23,769 some action from it is it's just that 707 00:25:23,770 --> 00:25:25,869 it's a lot easier to reason about if you 708 00:25:25,870 --> 00:25:28,539 have something like it to do primitive 709 00:25:28,540 --> 00:25:30,339 and you're trying to wrap your head 710 00:25:30,340 --> 00:25:31,340 around it. 711 00:25:33,740 --> 00:25:35,839 OK, are there are there 712 00:25:35,840 --> 00:25:37,579 any more questions from the Internet, 713 00:25:37,580 --> 00:25:39,019 Angel? Yes, there is. 714 00:25:39,020 --> 00:25:40,879 OK, I'll ask away. 715 00:25:40,880 --> 00:25:43,189 Um, Twilight Sparkle for my 716 00:25:43,190 --> 00:25:45,649 he asks, do you think a game in 40 717 00:25:45,650 --> 00:25:46,939 plus would be possible? 718 00:25:46,940 --> 00:25:48,589 And do you think it would be playable? 719 00:25:52,160 --> 00:25:54,439 So there actually are 720 00:25:54,440 --> 00:25:55,879 games in 40 and higher. 721 00:25:55,880 --> 00:25:57,639 I remember at least a game called 40 722 00:25:57,640 --> 00:26:00,169 Mays, and there's a couple of adaptations 723 00:26:00,170 --> 00:26:02,389 of the Rubik's Cube to at least 40, 724 00:26:02,390 --> 00:26:03,890 50. And I think I've seen 70 725 00:26:06,050 --> 00:26:07,339 with Rubik's Cube in particular. 726 00:26:07,340 --> 00:26:08,749 I have to admit that I can solve a pretty 727 00:26:08,750 --> 00:26:09,199 one. 728 00:26:09,200 --> 00:26:10,200 So 729 00:26:11,750 --> 00:26:13,849 I would be amazed to see anyone solve a 730 00:26:13,850 --> 00:26:15,979 forty one. But it's possible 731 00:26:15,980 --> 00:26:16,909 and it can be done. 732 00:26:16,910 --> 00:26:18,829 So actually when one when I was thinking 733 00:26:18,830 --> 00:26:21,049 about doing this stuff, the 734 00:26:21,050 --> 00:26:22,849 transformations kind of look really cool 735 00:26:22,850 --> 00:26:24,769 and it would be kind of cool to use it as 736 00:26:24,770 --> 00:26:27,139 like a transformation effect. 737 00:26:27,140 --> 00:26:28,729 Like you have your scene and you have no 738 00:26:28,730 --> 00:26:30,889 see and then you can do a 40 swap 739 00:26:30,890 --> 00:26:33,259 over, which I think would be really cool. 740 00:26:33,260 --> 00:26:34,819 But I'm not sure, like, 741 00:26:35,960 --> 00:26:38,839 I would love to see more games like this. 742 00:26:38,840 --> 00:26:41,359 And there are some, but and. 743 00:26:41,360 --> 00:26:42,360 Yeah. 744 00:26:45,350 --> 00:26:47,809 OK, are there more intimate questions? 745 00:26:48,960 --> 00:26:51,139 Not so far. OK, 746 00:26:51,140 --> 00:26:53,119 one more microphone number three. 747 00:26:53,120 --> 00:26:54,919 Thank you for your talk. 748 00:26:54,920 --> 00:26:57,199 I have one question regarding 749 00:26:57,200 --> 00:27:00,409 using it, not just those factors, 750 00:27:00,410 --> 00:27:02,509 but just inserting 40 or 751 00:27:02,510 --> 00:27:04,579 indeed datasets 752 00:27:04,580 --> 00:27:06,289 from real data. 753 00:27:06,290 --> 00:27:08,129 And does it work? 754 00:27:08,130 --> 00:27:10,519 And how would 755 00:27:10,520 --> 00:27:12,709 maybe look like and what trick 756 00:27:12,710 --> 00:27:15,319 you used to get the transparency 757 00:27:15,320 --> 00:27:17,640 effect for this data center? 758 00:27:19,550 --> 00:27:21,619 So, I mean, in the demo, 759 00:27:21,620 --> 00:27:23,689 I, um, I 760 00:27:23,690 --> 00:27:25,999 mean, I basically just use a transfer 761 00:27:26,000 --> 00:27:28,159 to the surface that that part was 762 00:27:28,160 --> 00:27:30,379 easy. But I could 763 00:27:30,380 --> 00:27:32,869 see this use in the higher dimensions 764 00:27:32,870 --> 00:27:34,309 to visualize data sets. 765 00:27:34,310 --> 00:27:36,589 So, I mean, when you're looking 766 00:27:36,590 --> 00:27:38,929 at a lot of a lot of stuff where you 767 00:27:38,930 --> 00:27:40,939 where you analyze stuff into into 768 00:27:40,940 --> 00:27:43,129 different categories, you always end 769 00:27:43,130 --> 00:27:44,269 up with more on free. 770 00:27:44,270 --> 00:27:46,309 So if you would like to draw a graph, it 771 00:27:46,310 --> 00:27:48,529 would probably be very 772 00:27:48,530 --> 00:27:50,089 easy to make a plan or one in three 773 00:27:50,090 --> 00:27:51,079 dimensions. 774 00:27:51,080 --> 00:27:54,109 But I've not seen this done yet. 775 00:27:54,110 --> 00:27:56,419 I would love to see this done. 776 00:27:56,420 --> 00:27:58,489 But unfortunately, it is kind of hard to 777 00:27:58,490 --> 00:28:00,379 wrap your head around a 40 rotation part. 778 00:28:00,380 --> 00:28:02,449 So I'm not sure 779 00:28:02,450 --> 00:28:04,159 if because we've got so used to make 780 00:28:04,160 --> 00:28:05,749 stuff easier to see. 781 00:28:05,750 --> 00:28:07,339 So I'm not sure if it will make it easier 782 00:28:07,340 --> 00:28:09,709 to see if you're not trying to see me, 783 00:28:09,710 --> 00:28:10,729 but it would probably be cool. 784 00:28:13,670 --> 00:28:15,889 OK, we have time up for about 785 00:28:15,890 --> 00:28:17,269 one or two more questions. 786 00:28:17,270 --> 00:28:18,709 Let's try microphone number two for a 787 00:28:18,710 --> 00:28:19,999 change, please. 788 00:28:20,000 --> 00:28:21,349 Thank you for the talk. 789 00:28:21,350 --> 00:28:23,179 I have some sort of more theoretical 790 00:28:23,180 --> 00:28:24,199 question I was wondering. 791 00:28:24,200 --> 00:28:26,239 You told us that there are forty seven 792 00:28:26,240 --> 00:28:28,279 types of variations and I've never heard 793 00:28:28,280 --> 00:28:29,509 of variations. 794 00:28:29,510 --> 00:28:31,699 So what actually do they have some 795 00:28:31,700 --> 00:28:33,469 sort of properties? It's kind of a very 796 00:28:33,470 --> 00:28:34,549 small class. 797 00:28:34,550 --> 00:28:36,649 Um, so they're just they're 798 00:28:36,650 --> 00:28:38,809 just basically defined at 799 00:28:38,810 --> 00:28:41,059 the end of that particular paper 800 00:28:41,060 --> 00:28:43,259 with the severo here. 801 00:28:43,260 --> 00:28:45,499 So this particular paper 802 00:28:45,500 --> 00:28:47,250 so very specifically defined a 803 00:28:48,290 --> 00:28:50,479 fairly common property they really have 804 00:28:50,480 --> 00:28:52,399 is that they're sort of esthetically 805 00:28:52,400 --> 00:28:54,589 pleasing on their own and 806 00:28:54,590 --> 00:28:56,739 that they're all tuti so. 807 00:28:56,740 --> 00:28:57,949 So you can extend some of them. 808 00:28:57,950 --> 00:28:59,419 You can extend numbers, but they're 809 00:28:59,420 --> 00:29:01,129 specifically defined in the appendix of 810 00:29:01,130 --> 00:29:02,149 that paper. 811 00:29:02,150 --> 00:29:03,150 OK, thank you very much. 812 00:29:05,600 --> 00:29:07,619 OK, one last question. 813 00:29:07,620 --> 00:29:09,229 Yes, not a question. 814 00:29:09,230 --> 00:29:11,359 Just a quick info 815 00:29:11,360 --> 00:29:13,019 on the 40 games question. 816 00:29:13,020 --> 00:29:14,539 So there is a game that made the rounds 817 00:29:14,540 --> 00:29:16,609 on the Internet this year called, and 818 00:29:16,610 --> 00:29:18,019 I have no clue where the word comes from, 819 00:29:18,020 --> 00:29:20,719 so I can't pronounce it mega churi. 820 00:29:20,720 --> 00:29:23,179 Am I a k 821 00:29:23,180 --> 00:29:24,739 u r e? 822 00:29:24,740 --> 00:29:25,970 You can look it up and 823 00:29:27,320 --> 00:29:29,299 what you can do in that game is like you 824 00:29:29,300 --> 00:29:31,339 have a 3D environment, you look at it in 825 00:29:31,340 --> 00:29:34,369 the 3D sense and then like you 826 00:29:34,370 --> 00:29:36,739 get to a wall and in your dimension 827 00:29:36,740 --> 00:29:38,239 that you're currently in, you can't walk 828 00:29:38,240 --> 00:29:40,879 around the wall and then you can shift 829 00:29:40,880 --> 00:29:43,099 to the fourth dimension or into 830 00:29:43,100 --> 00:29:45,409 another version of your 3D world 831 00:29:45,410 --> 00:29:47,209 along the fourth axis. 832 00:29:47,210 --> 00:29:49,609 And then you can go around 833 00:29:49,610 --> 00:29:50,599 the wall. 834 00:29:50,600 --> 00:29:52,759 And in gameplay terms, 835 00:29:52,760 --> 00:29:54,649 it's really just that you shift to 836 00:29:54,650 --> 00:29:56,209 another dimension. I mean, a lot of games 837 00:29:56,210 --> 00:29:58,309 do that. But the funny thing is that 838 00:29:58,310 --> 00:30:00,349 that game actually implements it with the 839 00:30:00,350 --> 00:30:02,269 correct math. So it looks really, really 840 00:30:02,270 --> 00:30:02,839 fancy. 841 00:30:02,840 --> 00:30:05,089 I remember seeing that I haven't 842 00:30:05,090 --> 00:30:06,709 tried it. I wanted to try it. 843 00:30:06,710 --> 00:30:09,289 So, I 844 00:30:09,290 --> 00:30:11,479 mean, it makes sense 845 00:30:11,480 --> 00:30:13,459 that it works because, well, when you do 846 00:30:13,460 --> 00:30:15,559 40 projects, you really end up with the 847 00:30:15,560 --> 00:30:17,449 free world. So it totally makes sense 848 00:30:17,450 --> 00:30:19,549 that you could use this to 849 00:30:19,550 --> 00:30:21,199 turn parts of the world around. 850 00:30:21,200 --> 00:30:23,269 So I've seen it look very cool, 851 00:30:23,270 --> 00:30:25,549 but I've tried it, but 852 00:30:25,550 --> 00:30:26,550 probably. Well, 853 00:30:28,710 --> 00:30:30,859 uh, let's thank the speaker 854 00:30:30,860 --> 00:30:31,860 again, please.