PythagorasTree vs Every Possible Picture

The Pythagoras Tree is math art. A square trunk is drawn. The hypotenuse of a right triangle is laid on top of the square. From the two legs two new squares are drawn. This process is repeated recursively until there the size of the square is too small to draw. Here you can adjust the angles of the triangle and the color of the tree. You can also make the tree grow and shrink to see the steps in making the tree.

Digital media can only display a finite number of images, limited by the resolution of the screen. This app will display them all, at resolutions set by the user. If you're not doing anything else for geologic time, you might enjoy this. You can set the number of colors (or grays) from 2 to 256 and the resolution from 8x8 to 64x64. There are 3 algorithms for displaying the pictures: Center (growing out from the middle of the screen), Permute (changes happen at randomly chosen pixels), or Shuffle (the entire screen is shuffled after each picture is displayed). By default the app starts from a black screen, but you can also choose white or a screen in which each pixel has a random color. And because displaying all the possible pictures takes a very long time, you can get a headstart by having the app pretend it's been running since the birth of the universe.