Emergence 2009: 1D Cellular Automaton Variant III
Biology 361 = Computer Science 361
Bryn Mawr College, Spring 2009
|WHAT IS IT?|
|This model is an example of a one-dimensional cellular automata. There are in total 256 possible one-dimensional cellular automata and this one models "rule 105". Cellular automata are simple programs which interestingly produce quite complicated behavior. They consist of cells, represented in this case by patches, and have two possible states: "on" or "off". These states are represented by colors, in this case: black and green, green signifies "on" and black signifies "off". The cellular automata starts of with a single row of cells and at every step there is a rule that determines the color of the cell below based on the color of the given cell and the colors of its immediate left and right neighbors. Since there are two possible states for each cell and three cells that determine the behavior of the next cell there are 2 x 2 x 2 = 8 possible combinations of colors of a cell and its two neighbors there have to be eight rules to specify the next cell given these eight different conditions. A particular set of eight rules specify one of the 256 one-dimensional cellular automata.|
|HOW IT WORKS
|Cellular automata 105 consists of a set of eight rules given a cell and its left and right immediate neighbors. For example, one rule states that if a patch is black and its left and right neighbors are black then the patch below will turn green. There are eight rules of this nature.|
|HOW TO USE IT|
The SETUP button creates one green patch in the first row.
The GO button creates the next row of cells based on the state of the previous row of cells and the rules of the cellular automata.
The GO-FOREVER button repeats the GO procedure continuously.
The SELECTROW slider allows you to select a certain row of cells.
The SETUP-CONTINUE button copies the selected row to the top and runs the model from that row onward.
|THINGS TO NOTICE|
What is interesting about this rule is that the left and right half of the larger triangle seem symmetrical and there appear to be repeating patterns within these larger triangles.
Do you notice any patterns or common themes recurring in this model? What are they? While we can detect patterns at a larger scale would it be possible to predict the next row of cells given the previous rows?
|THINGS TO TRY|
The SELECTROW slider is interesting because it allows you to have more patches in the first row instead of just a single patch. It also allow you to see what happens when the model wraps around vertically so that our visualization of the automata is not limited by screen size. What happens to the pattern given different numbers of starting patches? Do you notice any specific patterns develop as the cellular automata continues to grow vertically?
The LEFTNEIGHBOR and RIGHTNEIGHBOR switches allow you to see what happens when it is not the immediate neighbors, but rather neighbors further left or right of the center that influence the state of the patch below. What happens to the pattern as neighbors further from the center influence the patches below?
|EXTENDING THE MODEL
One way to extend this model would be to see what would happen if more than two color/ states are possible for the cells.
Another way to extend the model would be to see what would occur when more than just a cell and its two neighbors affect the state of the cell below. What if you took into account more neighbors?
|One of the important features to notice is that in NetLogo the models wrap around the horizontal axis. Since Wolfram's pictures of the models of cellular automata are based on an infinite grid they might look different from the NetLogo models.|
|The CA 1D Elementary, CA 1D Simple Examples, and CA 1D Totalistic models are important to take note of.|
|CREDITS AND REFERENCES
Von Neumann, J. and Burks, A. W., Eds, 1966. Theory of Self-Reproducing Automata. University of Illinois Press, Champaign, IL.
Toffoli, T. 1977. Computation and construction universality of reversible cellular automata. J. Comput. Syst. Sci. 15, 213-231.
Langton, C. 1984. Self-reproduction in cellular automata. Physica D 10, 134-144
Wolfram, S. 1986. Theory and Applications of Cellular Automata: Including Selected Papers 1983-1986. World Scientific Publishing Co., Inc., River Edge, NJ.
Bar-Yam, Y. 1997. Dynamics of Complex Systems. Perseus Press. Reading, Ma.
Wolfram, S. 2002. A New Kind of Science. Wolfram Media Inc. Champaign, IL.
Wilensky, U. (1998). NetLogo CA 1D Elementary model. http://ccl.northwestern.edu/netlogo/models/CA1DElementary . Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
Models created using NetLogo.