Adam Campbell's Website
1D continuous cellular automata

  • This type of cellular automata (CA) is a bit different from the discrete ones that are typically seen. This is a type of one-dimensional, continuous CA that works on values in the range of [0.0, 1.0). The CA begins with a single 1.0 in the middle of the lattice, and in the next time step, the value of each cell is averaged with the values of its left and right neighbors. This average is then added to the fractional value seen in the applet (which begins at 0.9.) Note, only the fractional value is used. For example, if the values of the three cells were 0.7, 0.8 and 0.9, we would first compute the average to be (0.7 + 0.8 + 0.9)/3 = 0.8 which we would then add to 0.9 to get 1.7. Finally, we remove any whole number part to obtain 0.7.
  • 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 length is 50,000 cells, and the row is actually circular (cell 1 is a neighbor of cell 50,000.)
  • This CA is presented on pages 155-160 of Stephen Wolfram's A New Kind of Science.
  • Click the box next to Restart to reset the applet.
  • Pause simply pauses the applet.
  • Click inside any of the 9 colored boxes to change the color of the newly drawn cells.
  • To change the fractional value that is added to the average of the three cells, click on the up and down arrows over each of the digits in the fraction.
Additional Information:
  • If you select a fractional value that creates a sharp contrast between the colors of consecutive 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