Cauchy problem for inviscid Burgers' equation is not "solvable" (globally) for many initial conditions...but we can depict the graph of the function that "could have been the solution"... (and the characteristic surface of course)

A sympy script in #obsidianmd. Powers of Arnold cat map matrix gives you FIbonacci coefficients and thus they grow exponentially...

Red: preimage of unit disk under a complex polynomial, or |p(z)|< 1
Violet, black: Curves defined by real and complex parts of p = 0 resp.