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| STARTER REDUX ARCHIEF (NL) International BLOG NL LOG SHOP monADs | |||||||
...again: lot's of interesting mail today... |
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21022006 From The Nonlinear Workbook by Willi-Hans Steeb ( ISBN 981-256-278-8 ) : One-dimensional maps 1.1 Exact and Numerical Trajectories
[Warning: the 'music' you are about to hear is rather irritating - mind your neighbours]
MINENONEMANEMU This flash animation moves to one of twelve frames dependent on the value of X%12
until the period orbit ...421421... is reached. While moving towards its period orbit it also stores the values in an array.
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<UNFOLD>
The function in grey above is a simple linear function, utterly predictable. Given a certain input, a real number, it will create a map of real numbers leading to its period orbit ...421421... by taking its output as new input for the same equation. This happens in fully predicatable manner. Nothing weird or nonlinear about it.
So there's no answers here and hardly any art, but i took it as a starting point for yet another string of things inside the Cathedral. Somehow i feel i have to learn about things like the Ruelle-Takens-Newhouse Scenario, Hopf Bifurcations and Heigway's Dragon, so if you're interested too, i'd be glad to take you along my dummie trail. Like most of you, i know next to nothing on these subjects, but I do know a tiny bit of coding so i 'll be very explicit about how to translate all the Mathematical Beauties to 'real world' java examples. Sure, this takes place within the Cathedral, so you may expect some irregularities along the path, and as you should know by now, nothing here gets completed or substantial without it proving it's worth to Our Lady Cathedral-Mother Dear. In other words, as usual, i start these things on stupid impulse, & no one can tell what may come of it. Now i know there do exist some good introductions out there, but i can't bring myself to going through all that, just reading it. I need to be doing something with it, otherwise i just clean forget everything i read. That, i think, about covers the Why of things. |
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There's a boring start to all subjects, so here's the 'Hello World' of (Non)linearity: the one-dimensional maps below take the instant of their creation as an input (request time of this file + the time it takes to compute the previous maps), effectively showing their computation takes time. Wow, spec - ta - cu - lar! Well, at least it clearly shows that linearity in functions doesn't lead to predictable outcomes when applied in the real world. Time is a nasty bugger and we need to keep a clear picture of things as they happen. Math is math, code is code, running code is running code and people discussing the real world all need to be addressed on their own plane of consistency. As you can see, a lot of things can happen between those spaces in a split second. Finally, visualisations like these may not give you a better understanding of the mathematics that underlie them, and math itself doesn't need it much or not at all, but they may be a welcome alternative to the tempting images of mystification that come to (my) mind (at least) when i think of the names mentioned above or hear someone mentioning them in real world language that he or she claims matters to me as well. If i don't understand, at least i can see what i don't understand. So perhaps this coding business is about a very private form of ownership or lack thereoff, after all. </UNFOLD> © dv 2006 - Free Art License - L.M. April 9, 2006 4:50 PM |
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<%@ page contentType="text/html;charset=utf-8" language="java"
import="java.math.*"%> |
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<% // first use a boolean to alternate tables boolean mod=true; StringBuffer sb=new StringBuffer(); for (int k=6;k>0;k--){
%> |
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//in one html table give results for f(x) with original input the time of the users request in Milliseconds sinds january 1 1970 descending to when the function reaches the period orbit ...421421... Date d=new Date(); String tijd=""+d.getTime(); BigInteger X= new BigInteger(tijd); BigInteger TWO= new BigInteger("2"); BigInteger THREE= new BigInteger("3"); int T=350; for (int t=0;t<T;t++){
} |
<% //in another table give the same results ascending for (int i=349;i>0;i--){
} %> |
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| <% }else{ mod=true; %> |
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<% //turn around the sequence of tables -first use what's still in the StringBuffer for descending output at the end of this table be sure to empty the StringBuffer thus sb.delete(0,sb.length()); //insert the art-code stuff anywhere between the tables //because the computation takes quite some time, you get different dates to refer to (ususally one second will elaps, if not, someone upgraded my server). Do not do this (a lot) on your site, the application server does not like all that work. //if you refresh the page a few times, you'll see that for some amount of milliseconds (the input), the function reaches its period orbid, for others it doesn't. It would, eventually if you change the iteration from 350 to sth higher, say 700. //in the next episode we'll start using Processing to avoid all of this Server Stress. Surprisingly, the user's computer can count too, so we don't need Big Mama. & JSP spaghetti is nice because it looks more complicated, but it's also unnecessarily confusing... }//you opened a for loop up there, remember? |
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CODE|ART is not a question |
Relevant Math articles in Wikipedia |
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3681767936488
1840883968244 920441984122 460220992061 1380662976184 690331488092 345165744046 172582872023 517748616070 258874308035 776622924106 388311462053 1164934386160 582467193080 291233596540 145616798270 72808399135 218425197406 109212598703 327637796110 163818898055 491456694166 245728347083 737185041250 368592520625 1105777561876 552888780938 276444390469 829333171408 414666585704 207333292852 103666646426 51833323213 155499969640 77749984820 38874992410 19437496205 58312488616 29156244308 14578122154 7289061077 21867183232 10933591616 5466795808 2733397904 1366698952 683349476 341674738 170837369 512512108 256256054 128128027 384384082 192192041 576576124 288288062 144144031 432432094 216216047 648648142 324324071 972972214 486486107 1459458322 729729161 2189187484 1094593742 547296871 1641890614 820945307 2462835922 1231417961 3694253884 1847126942 923563471 2770690414 1385345207 4156035622 2078017811 6234053434 3117026717 9351080152 4675540076 2337770038 1168885019 3506655058 1753327529 5259982588 2629991294 1314995647 3944986942 1972493471 5917480414 2958740207 8876220622 4438110311 13314330934 6657165467 19971496402 9985748201 29957244604 14978622302 7489311151 22467933454 11233966727 33701900182 16850950091 50552850274 25276425137 75829275412 37914637706 18957318853 56871956560 28435978280 14217989140 7108994570 3554497285 10663491856 5331745928 2665872964 1332936482 666468241 1999404724 999702362 499851181 1499553544 749776772 374888386 187444193 562332580 281166290 140583145 421749436 210874718 105437359 316312078 158156039 474468118 237234059 711702178 355851089 1067553268 533776634 266888317 800664952 400332476 200166238 100083119 300249358 150124679 450374038 225187019 675561058 337780529 1013341588 506670794 253335397 760006192 380003096 190001548 95000774 47500387 142501162 71250581 213751744 106875872 53437936 26718968 13359484 6679742 3339871 10019614 5009807 15029422 7514711 22544134 11272067 33816202 16908101 50724304 25362152 12681076 6340538 3170269 9510808 4755404 2377702 1188851 3566554 1783277 5349832 2674916 1337458 668729 2006188 1003094 501547 1504642 752321 2256964 1128482 564241 1692724 846362 423181 1269544 634772 317386 158693 476080 238040 119020 59510 29755 89266 44633 133900 66950 33475 100426 50213 150640 75320 37660 18830 9415 28246 14123 42370 21185 63556 31778 15889 47668 23834 11917 35752 17876 8938 4469 13408 6704 3352 1676 838 419 1258 629 1888 944 472 236 118 59 178 89 268 134 67 202 101 304 152 76 38 19 58 29 88 44 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4
4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 8 16 5 10 20 40 13 26 52 17 34 11 22 44 88 29 58 19 38 76 152 304 101 202 67 134 268 89 178 59 118 236 472 944 1888 629 1258 419 838 1676 3352 6704 13408 4469 8938 17876 35752 11917 23834 47668 15889 31778 63556 21185 42370 14123 28246 9415 18830 37660 75320 150640 50213 100426 33475 66950 133900 44633 89266 29755 59510 119020 238040 476080 158693 317386 634772 1269544 423181 846362 1692724 564241 1128482 2256964 752321 1504642 501547 1003094 2006188 668729 1337458 2674916 5349832 1783277 3566554 1188851 2377702 4755404 9510808 3170269 6340538 12681076 25362152 50724304 16908101 33816202 11272067 22544134 7514711 15029422 5009807 10019614 3339871 6679742 13359484 26718968 53437936 106875872 213751744 71250581 142501162 47500387 95000774 190001548 380003096 760006192 253335397 506670794 1013341588 337780529 675561058 225187019 450374038 150124679 300249358 100083119 200166238 400332476 800664952 266888317 533776634 1067553268 355851089 711702178 237234059 474468118 158156039 316312078 105437359 210874718 421749436 140583145 281166290 562332580 187444193 374888386 749776772 1499553544 499851181 999702362 1999404724 666468241 1332936482 2665872964 5331745928 10663491856 3554497285 7108994570 14217989140 28435978280 56871956560 18957318853 37914637706 75829275412 25276425137 50552850274 16850950091 33701900182 11233966727 22467933454 7489311151 14978622302 29957244604 9985748201 19971496402 6657165467 13314330934 4438110311 8876220622 2958740207 5917480414 1972493471 3944986942 1314995647 2629991294 5259982588 1753327529 3506655058 1168885019 2337770038 4675540076 9351080152 3117026717 6234053434 2078017811 4156035622 1385345207 2770690414 923563471 1847126942 3694253884 1231417961 2462835922 820945307 1641890614 547296871 1094593742 2189187484 729729161 1459458322 486486107 972972214 324324071 648648142 216216047 432432094 144144031 288288062 576576124 192192041 384384082 128128027 256256054 512512108 170837369 341674738 683349476 1366698952 2733397904 5466795808 10933591616 21867183232 7289061077 14578122154 29156244308 58312488616 19437496205 38874992410 77749984820 155499969640 51833323213 103666646426 207333292852 414666585704 829333171408 276444390469 552888780938 1105777561876 368592520625 737185041250 245728347083 491456694166 163818898055 327637796110 109212598703 218425197406 72808399135 145616798270 291233596540 582467193080 1164934386160 388311462053 776622924106 258874308035 517748616070 172582872023 345165744046 690331488092 1380662976184 460220992061 920441984122 1840883968244 |
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Fri Nov 21 09:26:19 CET 2008 & code is more important than art |
613627989516
306813994758 153406997379 460220992138 230110496069 690331488208 345165744104 172582872052 86291436026 43145718013 129437154040 64718577020 32359288510 16179644255 48538932766 24269466383 72808399150 36404199575 109212598726 54606299363 163818898090 81909449045 245728347136 122864173568 61432086784 30716043392 15358021696 7679010848 3839505424 1919752712 959876356 479938178 239969089 719907268 359953634 179976817 539930452 269965226 134982613 404947840 202473920 101236960 50618480 25309240 12654620 6327310 3163655 9490966 4745483 14236450 7118225 21354676 10677338 5338669 16016008 8008004 4004002 2002001 6006004 3003002 1501501 4504504 2252252 1126126 563063 1689190 844595 2533786 1266893 3800680 1900340 950170 475085 1425256 712628 356314 178157 534472 267236 133618 66809 200428 100214 50107 150322 75161 225484 112742 56371 169114 84557 253672 126836 63418 31709 95128 47564 23782 11891 35674 17837 53512 26756 13378 6689 20068 10034 5017 15052 7526 3763 11290 5645 16936 8468 4234 2117 6352 3176 1588 794 397 1192 596 298 149 448 224 112 56 28 14 7 22 11 34 17 52 26 13 40 20 10 5 16 8 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1 4 2 1
1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 1 2 4 8 16 5 10 20 40 13 26 52 17 34 11 22 7 14 28 56 112 224 448 149 298 596 1192 397 794 1588 3176 6352 2117 4234 8468 16936 5645 11290 3763 7526 15052 5017 10034 20068 6689 13378 26756 53512 17837 35674 11891 23782 47564 95128 31709 63418 126836 253672 84557 169114 56371 112742 225484 75161 150322 50107 100214 200428 66809 133618 267236 534472 178157 356314 712628 1425256 475085 950170 1900340 3800680 1266893 2533786 844595 1689190 563063 1126126 2252252 4504504 1501501 3003002 6006004 2002001 4004002 8008004 16016008 5338669 10677338 21354676 7118225 14236450 4745483 9490966 3163655 6327310 12654620 25309240 50618480 101236960 202473920 404947840 134982613 269965226 539930452 179976817 359953634 719907268 239969089 479938178 959876356 1919752712 3839505424 7679010848 15358021696 30716043392 61432086784 122864173568 245728347136 81909449045 163818898090 54606299363 109212598726 36404199575 72808399150 24269466383 48538932766 16179644255 32359288510 64718577020 129437154040 43145718013 86291436026 172582872052 345165744104 690331488208 230110496069 460220992138 153406997379 306813994758 |
1
Fri Nov 21 09:26:19 CET 2008 & code is more important than art |
613627989594
306813994797 920441984392 460220992196 230110496098 115055248049 345165744148 172582872074 86291436037 258874308112 129437154056 64718577028 32359288514 16179644257 48538932772 24269466386 12134733193 36404199580 18202099790 9101049895 27303149686 13651574843 40954724530 20477362265 61432086796 30716043398 15358021699 46074065098 23037032549 69111097648 34555548824 17277774412 8638887206 4319443603 12958330810 6479165405 19437496216 9718748108 4859374054 2429687027 7289061082 3644530541 10933591624 5466795812 2733397906 1366698953 4100096860 2050048430 1025024215 3075072646 1537536323 4612608970 2306304485 6918913456 3459456728 1729728364 864864182 432432091 1297296274 648648137 1945944412 972972206 486486103 1459458310 729729155 2189187466 1094593733 3283781200 1641890600 820945300 410472650 205236325 615708976 307854488 153927244 76963622 38481811 115445434 57722717 173168152 86584076 43292038 21646019 64938058 32469029 97407088 48703544 24351772 12175886 6087943 18263830 9131915 27395746 13697873 41093620 20546810 10273405 30820216 15410108 7705054 3852527 11557582 5778791 17336374 8668187 26004562 13002281 39006844 19503422 9751711 29255134 14627567 43882702 21941351 65824054 32912027 98736082 49368041 148104124 74052062 37026031 111078094 55539047 166617142 83308571 249925714 124962857 374888572 187444286 93722143 281166430 140583215 421749646 210874823 632624470 316312235 948936706 474468353 1423405060 711702530 355851265 1067553796 533776898 266888449 800665348 400332674 200166337 600499012 300249506 150124753 450374260 225187130 112593565 337780696 168890348 84445174 42222587 126667762 63333881 190001644 95000822 47500411 142501234 71250617 213751852 106875926 53437963 160313890 80156945 240470836 120235418 60117709 180353128 90176564 45088282 22544141 67632424 33816212 16908106 8454053 25362160 12681080 6340540 3170270 1585135 4755406 2377703 7133110 3566555 10699666 5349833 16049500 8024750 4012375 12037126 6018563 18055690 9027845 27083536 13541768 6770884 3385442 1692721 5078164 2539082 1269541 3808624 1904312 952156 476078 238039 714118 357059 1071178 535589 1606768 803384 401692 200846 100423 301270 150635 451906 225953 677860 338930 169465 508396 254198 127099 381298 190649 571948 285974 142987 428962 214481 643444 321722 160861 482584 241292 120646 60323 180970 90485 271456 135728 67864 33932 16966 8483 25450 12725 38176 19088 9544 4772 2386 1193 3580 1790 895 2686 1343 4030 2015 6046 3023 9070 4535 13606 6803 20410 10205 30616 15308 7654 3827 11482 5741 17224 8612 4306 2153 6460 3230 1615 4846 2423 7270 3635 10906 5453 16360 8180 4090 2045 6136 3068 1534 767 2302 1151 3454 1727 5182 2591 7774 3887 11662 5831 17494 8747 26242 13121 39364 19682 9841 29524 14762 7381 22144 11072 5536 2768 1384 692 346 173 520 260 130 65 196 98 49 148 74 37 112 56 28 14 7 22 11 34 17 52
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52
Fri Nov 21 09:26:19 CET 2008 & code is more important than art |
If you have the time, please place comments on the no comments place please |
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| STARTER REDUX ARCHIEF (NL) International BLOG NL LOG SHOP monADs | |||||||
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