- 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
- 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.
- 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 firstname.lastname@example.org if you have any