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Craige_Hales
Super User
Mandelbrot shallow tour

JSL for the video.

picpath = ""; // "D:\Chales\pic\m";
//http://www.fractalforums.com/mandelbrot-and-julia-set/good-coordinates-for-mandelbrot-zooms/
//
//Points on the boundary of the Mandelbrot set generally have the most interesting orbits.  The easiest boundary points to compute are:
//
//* the spike along the negative real axis
//* the boundary of the main cardioid: r = (1 - cos(theta))/2, x = r*cos(theta)+0.25, y = r*sin(theta)
//* the boundary of the period 2 disk: r = 0.25, x = r*cos(theta)-1, y = r*sin(theta)
eps = 1.6; // slightly outside
deep = 10;
steps = 8000;
angle = 3;
scale = 2; // <<<<<<< video made with 20, very slow
xsize = 192 * scale;
ysize = 108 * scale;
diag = Sqrt( xsize ^ 2 + ysize ^ 2 );
mat = J( ysize, xsize, . );
New Window( "mandelbrot", bb = Border Box( Text Box( "wait" ) ) );
Wait( .2 );
num = 1e6;
For( t = 0, t < steps, t += 1,
	If( eps > 1e-9, eps *= .997 );
	deep += .3;
	angle += eps / 50;
	radius = (1 - Cos( angle )) / 2 + eps;
	x = radius * Cos( angle ) + 0.25;
	y = radius * Sin( angle );
	top = y - eps;
	bottom = y + eps;
	left = x - eps * xsize / ysize;
	right = x + eps * xsize / ysize;
	d = Floor( Min( 1e5, deep ) );
	Parallel Assign( {d = d}, mat[r( top, bottom ), c( left, right )] = Mandelbrot( d, 4, c, r ) );
	mat = mat / d;
	red = mat ^ .5;
	green = mat ^ 9;
	both = Loc( red :* green == 1 );
	red[both] = .1;
	green[both] = .4;
	blue = 1 - mat ^ .2;
	blue[both] = .1;
	img = New Image( "rgb", {red, green, blue} );
	(bb << child) << delete;
	bb << append( img );
	num += 1;
	If( picpath != "", img << saveimage( picpath || Char( num ) || ".png" ) );
	bb << updatewindow;
	Wait( 0 );
);

Last Modified: Mar 16, 2018 1:23 PM
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