I've opened http://trac.sagemath.org/sage_trac/ticket/11837 for adding Newton basin fractals to Sage. It turns out that even I could modify complex_plot to create these, after a few false steps. Sage-edu fans will perhaps be interested in this - if you've ever played with something like http://aleph0.clarku.edu/~djoyce/newton/newtongen.html, you will like this proof of concept. (The sage-edu post can end here :) but most will read on.)
However, it is super slow, because my Cython is very bad. The image at #11837 took a few minutes to produce on my reasonably new laptop. That's not even close to good enough. So anyone who is interested in adding more of this sort of thing to Sage, and making it good enough to actually use in real time and with more than a few plot points, or anyone who wants to show off their Cython-fu, please help! I've tried to emulate Joyce's algorithm in a very naive way, so it's also possible I've just done something really silly in checking when you're "in" a basin for sure. Next step is keeping track of the number of iterations it takes, which hopefully wouldn't slow it down much, and then could be added in as a multiplier to the color to make the nice shaded versions we are used to being spoiled with. And of course choosing a better interpolation for matplotlib.imshow() - I just picked the one that would be clearest, for now. Thanks for any comments or help. I'm hoping to use this in a course the second half of the semester - one intended (among other things) to familiarize majors with many tools and resources in math, such as MathSciNet, various journals, LaTeX, and... Sage. - kcrisman -- You received this message because you are subscribed to the Google Groups "sage-edu" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sage-edu?hl=en.
