Thanks! As a pupil in the 80s I experimented calculating the Mandelbrot set and looked into the algebraic formula of the cardioid to save compute time (10s of minutes then) in the boring non-divergent part. My math skills were too low to properly understand it then, but your article made me look it up and let me find http://cosinekitty.com/mandel_orbits_analysis.html . It's also interesting how much of the marketing aesthetics around chaos theory is based on relatively simple things like the behavior of squaring complex numbers and combining several things (up to fancy color schemes). Your article also made me quickly install xfractint again and draw a KAM torus, which happens to be one of my favorites.
Btw, learning about Muller's Recurrence via https://archive.is/K2TX3 I ask myself if there is a connection between the suitability of using non-floatingpoint methods and dynamic iterative systems?
Man you should also post about the kind of music you hear and heard ( in the past during your early years into programming ). It looks like you're on a song. Math-Breeze. And we're loving it.
Here's another cool animation - the impact of shifting the starting point (z0) for Mandelbrot set:
https://vimeo.com/936068771/14ff98eadb
PS. If you liked the f(z) = z^2 video toward the end of the article, you might also enjoy playing with this interactive conformal map demo done by another person: http://www.rotormind.com/projects/portfolio/codework/conformal/
Thanks! As a pupil in the 80s I experimented calculating the Mandelbrot set and looked into the algebraic formula of the cardioid to save compute time (10s of minutes then) in the boring non-divergent part. My math skills were too low to properly understand it then, but your article made me look it up and let me find http://cosinekitty.com/mandel_orbits_analysis.html . It's also interesting how much of the marketing aesthetics around chaos theory is based on relatively simple things like the behavior of squaring complex numbers and combining several things (up to fancy color schemes). Your article also made me quickly install xfractint again and draw a KAM torus, which happens to be one of my favorites.
Btw, learning about Muller's Recurrence via https://archive.is/K2TX3 I ask myself if there is a connection between the suitability of using non-floatingpoint methods and dynamic iterative systems?
Really cool! Thanks for doing all of this work and sharing it.
Man you should also post about the kind of music you hear and heard ( in the past during your early years into programming ). It looks like you're on a song. Math-Breeze. And we're loving it.