Chillheimer
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« Reply #15 on: June 19, 2015, 01:45:07 PM » |
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come on, lets do this in 3d. and as a movie!°! oh wait, I already did..
https://www.youtube.com/v/DxkAUz6VW6g&rel=1&fs=1&hd=1I rendered this short movie a few weeks ago and hadn't released it. somewhere in in amazing box, combined with amazing box SSE 2 your last pic reminded me of it. nice "coincidence" that those structures look so similar..
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« Last Edit: June 19, 2015, 02:04:57 PM by Chillheimer »
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--- Fractals - add some Chaos to your life and put the world in order. ---
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panzerboy
Fractal Lover
Posts: 242
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« Reply #16 on: June 19, 2015, 01:51:03 PM » |
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This video is private ?!
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Chillheimer
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« Reply #17 on: June 19, 2015, 02:04:35 PM » |
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This video is private ?!
stupid me... set it to public. thx for ppointing that out. edit: to make this post less useless, I'll add this little gem that I stumbled upon in the youtube recomendations:
https://www.youtube.com/v/RnGPpjvugZo&rel=1&fs=1&hd=1 hm, this guy has got a few other nice videos on his channel https://www.youtube.com/user/ch3trash0/videos
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« Last Edit: June 19, 2015, 02:16:01 PM by Chillheimer »
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--- Fractals - add some Chaos to your life and put the world in order. ---
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bkercso
Fractal Lover
Posts: 220
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« Reply #18 on: June 20, 2015, 01:47:05 AM » |
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Your render @00:25 looks like a big skyscraper.
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bkercso
Fractal Lover
Posts: 220
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« Reply #19 on: June 21, 2015, 12:42:55 AM » |
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I give the equations of bouncing ball on twin slope (double slope), because the .pdf I linked first is not the book itself, only a review. I wrote it in pascal language, so I use something similar now too. Variables: a: angle of slopes (alpha, 0..pi/2 [rad]) u: velocity component of the ball parallel with slope (0..1) z: square of velocity component of the ball perpendicular to slope (approx. 0..0.3) (mass of ball = gravity = 1)Iterate:
if u-2*sqrt(z)*tg(a)+sqrt(1-z)>=0 then u:=u-2*sqrt(z)*tg(a) {stay on current slope} else begin {jump to other slope} z_prev:=z; z:=-z*(1+0.5*sin(4*a)*tg(a))-u^2*0.5*sin(4*a)*ctg(a)+u*sqrt(z)*sin(4*a)+2*cos(a)^2; u:=-u+sqrt(z_prev)*tg(a)-sqrt(z)*tg(a); end;
I optimised it for faster running: cosa2:=cos(a)^2; sin4a:=sin(4*a); tga:=tg(a); ctga:=ctg(a); jumped:=false; temp0:=sqrt(1-z);
iteration begin if not(jumped) then begin sqrtz:=sqrt(z); temp1:=sqrtz*tga; end; jumped:=false; temp2:=2*temp1; temp3:=u-temp2; if temp3>=-temp0 then u:=temp3 {stay on current slope} else begin {jump to other slope} temp4:=0.5*sin4a; temp5:=u*temp4; z:=-z*(1+temp4*tga)+temp5*(-u*ctga+2*sqrtz)+2*cosa2; jumped:=true; temp0:=sqrt(1-z); sqrtz:=sqrt(z); temp1_:=temp1; temp1:=sqrtz*tga; u:=-u+temp1_-temp1; end; iteration end;
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bkercso
Fractal Lover
Posts: 220
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« Reply #20 on: June 21, 2015, 01:29:50 AM » |
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Quasy periodic zooms follow. Img #6 Seems like a digital microchip... alpha=60°, u(initial)=0.3, changed z, plotted z Set: Zoom: 130,000x zoom, 20 min calc. time, average 7 points/pixel (you cannot see the underlying structure if iterate more) Img #7alpha=60°, changed z, plotted u I also changed u(initial), because I noticed that the degree of quasy periodicity depends on the angle of initial velocity to slope, so I kept this angle constant. u(initial)=sqrt(z)*0.23 (remember: z is velocity^2 like quantity) Set: Zoom: strange that it shows blurred patterns. I think it is countured (quasy periodic) and blurred (chaotic) regions densely embedded in each other... 14000x zoom, 40 min calc. time
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« Last Edit: June 25, 2015, 11:06:44 AM by bkercso »
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bkercso
Fractal Lover
Posts: 220
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« Reply #21 on: June 21, 2015, 07:06:55 PM » |
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Img #8Set: Zoom: 1.3E7x zoom, 13 points/pixel, 8 hours
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« Last Edit: July 01, 2015, 03:05:14 PM by bkercso »
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bkercso
Fractal Lover
Posts: 220
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« Reply #22 on: June 22, 2015, 12:00:59 PM » |
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Img #9Set: Zoom: Some filaments. Changed z, plotted u. Average 170 points/pixel, 1E4x zoom, 24 hours calculation.
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« Last Edit: June 22, 2015, 09:54:22 PM by bkercso »
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Chillheimer
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« Reply #23 on: June 22, 2015, 12:21:49 PM » |
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hey bkercso, thx for sharing the equations. i wonder: is there something "more userfriendly" ? I'm no programmer and have no idea what to do with that code to get a picture. but I'd love to zoom around in some bifurcation diagrams..
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--- Fractals - add some Chaos to your life and put the world in order. ---
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bkercso
Fractal Lover
Posts: 220
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« Reply #24 on: June 22, 2015, 01:09:49 PM » |
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Hi, Uhh, my comments and some of my variables are in Hungarian, and you can use my code under freePascal compiler. In it's current form cannot compile an .exe from it because you can set parameters in declaration section. I use this as follows: generate a fractal, program writes point density by pixel in a .txt. With an other program (wrote in Delphi) convert it to .bmp. After that open the picture with IrfanView, select an area of it and typeing the four number from window header to my program to zoom. Not so user friendly.
But if somebody feel like and have enought time to write a software for bifurcation fractals I give the whole code and needed support with pleasure.
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bkercso
Fractal Lover
Posts: 220
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« Reply #25 on: June 22, 2015, 03:37:38 PM » |
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Just I searched fractal software which can render bifurcation maps and I'm surprised that I did not find one.
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bkercso
Fractal Lover
Posts: 220
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« Reply #26 on: June 22, 2015, 09:07:04 PM » |
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Img #10: Chinese pillars with baobab like-roots. We saw similar structures at double pendulum in the other topic. (The slow quasy periodic to chaotic transition mustache is also common in both fractals, but this is not seen in this zoom.) The common procedure in both case that an angle was changed along x-axis. Here I changed alpha from 59° to 61°. For fix z and u I used a map with changed z. u value selected from video I linked before. Set: Zoom:
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« Last Edit: July 06, 2015, 09:51:44 PM by bkercso »
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bkercso
Fractal Lover
Posts: 220
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« Reply #27 on: June 23, 2015, 09:35:28 AM » |
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Img #11: Blurred patterns of Img #7. I was right, these are densly packed quasy periodic and chaotic regions. So beauty... Set: Zoom: 1.5E5x zoom, 8 points/pixel, 23 hours And I'm working on make my softver usable before share it...
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« Last Edit: June 30, 2015, 03:53:52 PM by bkercso »
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Chillheimer
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« Reply #28 on: June 23, 2015, 10:13:51 AM » |
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But if somebody feel like and have enought time to write a software for bifurcation fractals I give the whole code and needed support with pleasure.
That's very generous! Thank you! Now I really hope that someone takes up that challenge...
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--- Fractals - add some Chaos to your life and put the world in order. ---
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bkercso
Fractal Lover
Posts: 220
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« Reply #29 on: June 23, 2015, 12:12:23 PM » |
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Yes, but did you read my last sentence below the pictures?
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