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The process is simply: 1. Take a plane 2. Cut out a shape 3. Make it a little taller 4. Repeat

• Similar to the spherical landscape algorithm by Hugo Elias.
• I found a combination of Ovals and Triangles to produce the best results.
Python, 117 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117``` ```#!/usr/bin/env python # -*- coding: utf-8 -*- import Image, ImageDraw, ImageChops, ImageOps, ImageFilter import pygame.display, pygame.image import random import sys from math import ceil percentWater = .70 mapSize = 600 #in pixels maxSize = 1.40 # 1 to 5 How big should the slices be cut, smaller slices create more islands, larger slices create less shape = 1.40 # 1 mean roundish continents .5 is twice as tall as it is wide, 2.0 is twice as wide as tall driftRate = .70 # As the world ages how much slower does it drift. 1 creates a more textured world but takes longer roughness = 1 #High numbers make a world faster, with more "ridges", but also makes things less "smooth" filename = 'heightmap.bmp' xrand = lambda ms = mapSize*3: int(randType(0, ms)) yrand = lambda ms = mapSize*2: int(randType(0-(ms/2), ms)) randType = random.uniform #change to alter variability def normalize(image): image = image.filter(ImageFilter.BLUR) picture = ImageChops.blend(ImageOps.equalize(image), image, .5) return ImageChops.multiply(picture, picture) def finish(image): #called when window is closed, or iterations stop picture = normalize(image) picture.save(filename) pygame.quit() sys.exit(); def drawPieSlices(oval, orig, action): fl = action[1] img = Image.new('L', (mapSize*2,mapSize)) draw = ImageDraw.Draw(img) draw.pieslice([oval[0],oval[1],mapSize*4,oval[3]], 90, 270, fill=fl) del draw orig = action[0](orig, img) img = Image.new('L', (mapSize*2,mapSize)) draw = ImageDraw.Draw(img) draw.pieslice([0-oval[0],oval[1],oval[2]-mapSize*2,oval[3]], 270, 90, fill=fl) del draw return action[0](orig, img) def drawOval(oval, orig, action): img = Image.new('L', (mapSize*2,mapSize)) draw = ImageDraw.Draw(img) draw.ellipse(oval, fill=action[1]) del draw return action[0](orig, img) def cutOval(orig, smallness=1): smallness = smallness ** driftRate landAction = lambda: ( ImageChops.add, ceil(randType(1,roughness*smallness*(percentWater))) ) seaAction = lambda: ( ImageChops.subtract, ceil(randType(1,roughness*smallness*(1.0-percentWater))) ) action = seaAction() if random.random() < percentWater else landAction() oval = [xrand(mapSize*2),yrand(mapSize),1,1] #x,y,x,y oval[2] = int(oval[0]+(mapSize*maxSize*shape)*smallness) oval[3] = int(oval[1]+(mapSize*maxSize)*smallness) if oval[2] > mapSize*2: #if x values cross our border, we needto wrap ret = drawPieSlices(oval, orig, action) else: ret = drawOval(oval, orig, action) return ret imageToPygame = lambda i: pygame.image.fromstring(i.tostring(), i.size, i.mode) def highestPointOnSphere(sphere): extremes = sphere.getextrema() return extremes[0]/255.0 if percentWater > .5 else 1-(extremes[1]/255.0) def createSphere(): pygame.init() #Need this to render the output sphere = Image.new('L', (mapSize*2,mapSize)) img = ImageDraw.Draw(sphere) baseline = (256*(1.0-(percentWater))) img.rectangle([0-mapSize,0,mapSize*4,mapSize], fill=baseline) del img return sphere def sphereToPicture(sphere): picture = normalize(sphere) picture = ImageOps.colorize(picture, (10,0,100), (0,256,0)) picture = imageToPygame(picture) return picture def generatePlanet(sphere, displayInterval = 50): extrema = highestPointOnSphere(sphere) i = 0 picture = sphereToPicture(sphere) pygame.display.set_mode(picture.get_size()) main_surface = pygame.display.get_surface() del picture while extrema > driftRate/(roughness*10*maxSize): sphere = cutOval(sphere, extrema) i = i+1 if displayInterval > 0 and i%displayInterval == 0: picture = sphereToPicture(sphere) main_surface.blit(picture, (0, 0)) pygame.display.update() del picture for event in pygame.event.get(): #When people close the window if event.type == pygame.QUIT: return image extrema = highestPointOnSphere(sphere) return sphere if __name__ == '__main__': finish(generatePlanet(createSphere(), 50)) ```

Edit: Recently improved the readability, efficiency, and effectivness of this algorithm. Try adjusting the variables at the top.

 Created by Shea Kauffman on Tue, 13 Oct 2009 (Apache)