Adam Campbell's Website
1D discrete cellular automata

  • A 1D cellular automata consists of a row of "cells" and a replacement rule. Each cell can be in one of two states: true/false, on/off, white/black, etc. Besides the middle, black cell, all of the cells in the initial row are white. From this simple initial configuration, we can see that complex behavior emerges from the simple replacement rule. The replacement rule works by simultaneously updating the color of each cell based on its color and the color of its left and right neighbors. The new row of cells is drawn below the old row, and this process repeats infinitely.
  • As you can see, the rows of cells expand infinitely, but because a computer does not have infinite memory, the row length must be finite. The row size is 50,000 cells, and the row is actually circular (cell 1 is a neighbor of cell 50,000.)
  • In Stephen Wolfram's "A New Kind of Science", you can read 1,000+ pages on cellular automata and other simple programs. Wolfram believes that the complexity that arises from simple programs like this are fundamental to all areas of science, and that the universe itself is just a simple cellular automata.
  • The rule numbers correspond to those on pages 55 and 56 of Wolfram's book.
  • Click the box next to Restart to start running the CA from the initial black cell.
  • Pause simply pauses the applet.
  • Init. random will randomly seed the initial configuration of the cells when the Restart box is pressed.
  • Click the eight boxes on the right of the arrows to change the replacement rule.
Additional Information:
  • In the future, I'd like to allow the user to change the color of the cells.
  • If you select a replacement rule that creates alternating black and white rows, you will probably see a lot of flickering due to the monitor rapidly switching back and forth between contrasting colors.
  • E-mail me at if you have any questions/comments