Oddbean new post about login | logout @b4c50e1b @218dc8a6 It is fun to experiment with other sets of coefficients too: https://kam.fit.cvut.cz/deploy/christensen/
@c30feace - nice! Is this page yours? The set I wrote about (K = 1, N → ∞) is connected. I like how some of the sets you drew are not. @218dc8a6 https://media.mathstodon.xyz/media_attachments/files/111/156/222/561/705/633/original/62c32cf8d64efde3.png
@b4c50e1b @218dc8a6 @5fb5d869 @6278416d Yes, I messed with it a few years ago. Source code is available on Github https://github.com/kalvotom/ChristensenSet.jl Of course, there are roots of polynomials up to some fixed degree, this is far from the limit 🙂. Also, the way you compose the final image plays a role (if I remember correctly, this is more like a density of roots, otherwise the picture would be huge). If you are interested in some particular section of the image, I might give it another try and produce it in more detail.
@c30feace @b4c50e1b @218dc8a6 hmm, if picking a different finite set of coefficients gives you a different fractal, what happens if you let a finite number of points wander continuously around the plane and make an animation of the results?
@088924ba - sounds fun, but it took Sam Derbyshire 4 days to generate this one picture using Mathematica, so to create a movie with many frames you'd have to lower the degree of the polynomial, only display a smaller region, get a better computer and/or be more clever about programming. This one picture was originally 5 gigabytes; this is a reduced version. @c30feace @218dc8a6 https://media.mathstodon.xyz/media_attachments/files/111/156/470/040/224/015/original/8ae93102c872d733.png
@b4c50e1b @088924ba @218dc8a6 My impression is that Mathematica is not well known for its fast numerical computations. That's why I tried Julia, out of curiosity. If I remember correctly, it was faster then days. Notice also, that I reached polynomials of higher degree. Anyway, gigabytes were indeed flying around 😂.
