Newton Basin Project

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 $\$g(z;k)\; \backslash equiv\; f(z)+u(|f(z)|-k-1)\; k\; Sin(z)\$$. This will yield the same roots as $\$f(z)=x^3-x\$$ on the real line. This obtains from Rouché's theorem as long as , $\$sin(z)\$$ being of bounded modulus there. Elsewhere the value can be seen as depending on the hyperbolic sine of the imaginary part of $\$z\$$, $\$sinh(\backslash Im\; z)\$$. Proof of which.