This program is inspired by Drow's Fractal World Generator, which is based on John Olsson's Fractal Worldmap Generator, which in turn claims to be based on a Voss fractal faulting algorithm
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This program:
Generates planes, of which each is defined by a random location in the sphere and a random direction on the sphere;
Generates a cylindrical map (either equal-area or equidistant) of pixels;
Back-projects each pixel of the map to the sphere; and
Increments the altitude of each pixel by 1 arbitrary unit for each plane in front of which the pixel lies.
(An erosion algorithm is pending.)
The difference between this algorithm and Drow's/Olsson's algorithm is that, because the planes need not pass through the center of the sphere, a promontory of elevation +N on one side of the planet need not be balanced by a depression of elevation −N on the other side of the planet.
The equidistant projection obviously should have an aspect ratio of 2 if you plan to use it as a sphere texture with a square graticule. If you seek to minimize shape distortion, Behrmann's equal-area projection, with its standard parallels of ±30 °, has an aspect ratio of 0.75π (approximately 2.356, or 7/3), and an equidistant projection with the same standard parallels has an aspect ratio of √(3) (approximately 1.732, or 7/4).
Blue pixels are in the lowest third of the range of altitudes, green pixels are in the middle third, and red pixels are in the top third. Thus, up to 765 levels (3 × 255) of altitude can be shown. (This is not the same as making the bottom third of pixels blue, the middle third of pixels green, and the top third of pixels red.)
The time required to create a map is proportional to the product of plane count, map width, and map height. A map with too many planes and/or pixels may freeze or crash your browser. However, you can navigate away to another tab while the program is working. The program will generate an alert (which should show up in your browser's list of tabs) when it's done with whatever you told it to do.
To download the image, right-click or long-press on it.