The equation for the mandelbrot set is z = z^2 + c,
in my exploration, I changed the values of c and analyzed the iteration in the table below
What algebriac patterns emerge in this table?
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2The equation cited is only part of the definition of the Mandelbrot set, which is: the set of complex $c$ such that the complex series defined by $z_0=0$, $z_{n+1}={z_n}^2+c$ is bounded as $n$ goes to infinity. By studying only real values of $c$, you are studying only the intersection of that set and the reals. Hint: prove that's a segment, and which. – fgrieu Mar 30 '23 at 06:45