Bifurcation Diagram Bouncing Ball

[Chillheimer]

nope i missed that! those pics are such a nice distraction

wohoo!
 

[lkmitch]

Just I searched fractal software which can render bifurcation maps and I'm surprised that I did not find one.

Ultra Fractal can, although it's not necessarily a simple thing to do.  Here's one of mine:

http://www.kerrymitchellart.com/gallery24/bifurcation.html

[bkercso]

Thx for the info. I didn't find much more pics with google.
But yours is a nice render!

[Softology]

Thanks for the inspiration bkercso.  I got back into my bifurcation code which was nothing more than a very pixelated black on white logistic renderer.  After some much needed updates in output quality and new fromuals here are some results.

Logistic Map




Henon Attractor




Delayed Logistic Map




Bouncing Ball






For full res images of the above see https://www.flickr.com/photos/39445835@N05/

I have included these new functions in the Bifurcation mode of Visions Of Chaos (http:/softology.com.au/voc.htm)

Jason.

[bkercso]

Wow, that's it! Thank you for sharing pics and also for the software.
My - far simpler - software is almost done, now writing some more help messages. I will share it in the next few days. But translating the code to English will take more time.

Regarding scale independent behavior of fractals try to use log scaling on parameter axis for undraw interesting sections.

[bkercso]

                 ***********************
The topic of my software Bifurcation Fractal Plotter is started!
http://www.fractalforums.com/windows-fractal-software/bifurcation-fractal-plotter-biffrapl/
                 ***********************

[bkercso]

Just I've made a series which tries reveal the structure of chaotic region, do this with increasing iteration number picture to picture.

Plotted z, changed alpha.
z=0.022, u=0.231 (fixed velocity-slope angle), alpha=59..61.
Iterations: 0.01, 0.3, 1, 3, 10, 30, 100, 300, 1000, 3000, 10000, 30000

Img #12

[bkercso]

Img #13
Patterns in hard chaotic regions:
The same image calculated with 8 digits and 20 digits variables. Conclusion: the blurred hard chaotic regions is own feature of this (these) system(s); the lack of contoured patterns do not come from calculation errors, not from finite precision of calculations!