The Mandelbrot Set

Charlene Chu - October 27, 2017

Here is a function we’ll use to create an interactive image of the Mendelbrot Set where we can zoom in.

activeZoomMS[p_]:=(Manipulate[
MandelbrotSetPlot[Apply[Complex,{p-α,p+α},{1}],
ColorFunction->"AvocadoColors",Frame->True,ImageSize->600],
{α,2,(10^(-4))}])

Here are some interesting points to zoom into. These are from https://www.wolfram.com/mathematica/new-in-10/enhanced-visualization/plot-the-mandelbrot-set.html

(* Seahorse Valley *)
(Subscript[p, 1])={-0.733,0.185};

(* smaller bulbs *)
(Subscript[p, 2])={0.2355,0.5617};

Here are some more interesting points to zoom into. These are from http://colinlmiller.com/fractals/gallery.htm

(* arm *)
(Subscript[p, 3])={-1.985540371654130485531439267191269851811165434636382820704394766801377,0.000000000000000000000000000001565120217211466101983496092509512479178};

(* curvy arm *)
(Subscript[p, 4])={-1.77810334274064037110522326038852639499207961414628307584575173232969154440,0.00767394242121339392672671947893471774958985018535019684946671264012302378};

Here is a spiral that I found.

(Subscript[p, 5])={0.236+27/152*0.001,0.563+57/152*0.001};

Here is another spiral point, but Mathematica cannot render the zoomed-in image as nicely...

(Subscript[p, 6])={0.2355+52/151*0.0005,0.5630+10/151*0.0005};

Use the function to zoom into the interesting points.

activeZoomMS[(Subscript[p, 6])]