Big Picture

[#1]

The JSL 2D matrix can be turned into an image using the NewImage function. 2D matrices and images use a lot of memory; you might be able to make a 30K x 30K matrix full of color values and display it. If you want to save it as a PNG file, you might need to try a smaller size; 20K x 20K worked for me. Here's some JSL with a comment about how you might avoid having multiple copies of the matrix in memory at once.

clear globals();

// notes on making big images
//
// a 20Kx20K matrix is 20000*20000*8/1024/1024/1024 = 3GB
// the image created from it will be at least half that size too, in memory.
// clear globals, above, makes sure old matrices are released, otherwise
// m=J(...) might have the old matrix in m on the left hand side while the
// new matrix is being created on the right hand side. Two copies at once.
// the parallel assign below is designed to do all the processing on an element.
// using m = f(m) later creates extra copies, and single-threaded. The
// commented-out range(m) was from previous runs to figure out the
// -1.1 and /1.5 scaling on the mandelbrot results. The critical
// part is making the RGB color from f1(m), f2(m), f3(m) inside the
// parallel assign. Otherwise there could be four! copies of m if
// newimage("rgb", {f1(m), f2(m), f3(m)})
// ---
// the above was important for a 30Kx30K matrix, using ~7GB; my machine
// could not hold ~28GB at once. But I had to reduce it to 20K anyway to
// save the picture; somewhere bigger than 20K refuses to save the image.

m = J( 20000, 20000, . );
Parallel Assign( {}, m[r( -1.5, 1.5 ), c( -2.25, 0.75 )] = //
	(//
		x = ((Mandelbrot( 10000, 0, c, r ) ^ .1) - 1.1) / 1.5 ; // scaled counts
		RGB Color( (x) ^ .5, (x) ^ 9, (1 - x) ^ 9 ) ; // keep final color
	)  //
);
//Show( Range( m ) ); // m holds JSL colors not mandelbrot counts. range is meaningless
m=newimage(m);

New Window( "m", m );
m<<savepicture("$desktop/mandelbrot.png","png");

There are two choices with NewImage: a single matrix containing JSL rgb colors, or three matrices of r, g, and b values between 0 and 1. The JSL shown uses the first choice because only one matrix needs to exist. The second choice is more flexible but will require, at least for a moment, four matrices to exist.

The attached picture is 20,000 by 20,000 pixels; depending on your viewer you'll want to scroll or zoom.