3 ms·

https://paulbourke.net/fractals/lyapunov/ https://paulbourke.net/fractals/lyapunov/ > It may diverge to infinity, for the range (+- 2) used here for each param

https://paulbourke.net/fractals/lyapunov/ https://paulbourke.net/fractals/lyapunov/ > It may diverge to infinity, for the range (+- 2) used here for each parameter this is the most likely event. These are also easy to detect and discard, indeed they need to be in order to avoid numerical errors. https://superliminal.com/fractals/bbrot/ https://superliminal.com/fractals/bbrot/ The above image shows the overall entire Buddhabrot object. To produce the image only requires some very simple modifications to the traditional mandelbrot rendering technique: Instead of selecting initial points on the real-complex plane one for each pixel, initial points are selected randomly from the image region or larger as needed. Then, each initial point is iterated using the standard mandelbrot function in order to first test whether it escapes from the region near the origin or not. Only those that do escape are then re-iterated in a second, pass. (The ones that don't escape - I.E. which are believed to be within the Mandelbrot Set - are ignored). During re-iteration, I increment a counter for each pixel that it lands on before eventually exiting. Every so often, the current array of "hit counts" is output as a grayscale image. Eventually, successive images barely differ from each other, ultimately converging on the one above. Is it possible to use the Buddhabrot technique on the lyapunov fractals ?

fractal4d 1y ago
Seems to me that the images on Bourke's site _are_ produced using the general "Buddhabrot" technique (splatting points onto an image). Although each image appears to only represent a single orbit sequence and the reject condition is inverted so that only stable orbits are shown. I've personally found the technique very versatile and have had a lot of fun playing around with it and exploring different variations. Was excited enough about the whole thing that I created a website for sharing some of my explorations: https://www.fractal4d.net/ https://www.fractal4d.net/ (shameless self-advertisement) With the exception of some Mandelbrot-style images all the rest are produced by splatting complex-valued orbit points onto an image in one way or another.

fractal4d 1y ago

Seems to me that the images on Bourke's site _are_ produced using the general "Buddhabrot" technique (splatting points onto an image). Although each image appears to only represent a single orbit sequence and the reject condition is inverted so that only stable orbits are shown. I've personally found the technique very versatile and have had a lot of fun playing around with it and exploring different variations. Was excited enough about the whole thing that I created a website for sharing some of my explorations: https://www.fractal4d.net/ https://www.fractal4d.net/ (shameless self-advertisement) With the exception of some Mandelbrot-style images all the rest are produced by splatting complex-valued orbit points onto an image in one way or another.