Processing math: 100%
Back
Close

Newton Basin Project

egoughnour
1,336 views
Previous: Colored By Iterations

Here is a slightly more interesting output

Note that u here is the Heaviside step function but it's applied to the (shifted) modulus of a function rather than a variable. That is, we are interested in roots of g(z;k)f(z)+u(|f(z)|k1)kSin(z). This will yield the same roots as f(z)=x3x on the real line. This obtains from Rouché's theorem as long as |f|<k, sin(z) being of bounded modulus there. Elsewhere the value can be seen as depending on the hyperbolic sine of the imaginary part of z, sinh(z). Proof of which.

Create your playground on Tech.io
This playground was created on Tech.io, our hands-on, knowledge-sharing platform for developers.
Go to tech.io
codingame x discord
Join the CodinGame community on Discord to chat about puzzle contributions, challenges, streams, blog articles - all that good stuff!
JOIN US ON DISCORD
Online Participants