Introduction to Wolfram's New Kind of Science: Cellular Automata
Ever wonder how some of the beautiful but complex patterns in nature can be produced? They often look like the painstaking work of a creative artist, but are are in fact the result of the repeated execution of a simple set of rules.
Stephen Wolfram introduces us to a set of cellular automata driven by two-hundred fifty-six rule sets. These rules govern whether a given pixel is colored based on the three pixels above it. Pixels in each row are calculated based on the row above. Click on the "Learn" button on the main menu screen for more information.
How to Use This Simulation
Start by clicking on "Learn," where we will take you through the concept of cellular automata.
Next, click on "Try It"and try out what different rules produce. You can type a number from 0 to 255 in the Rule# box, press "Run the Rule" and see what that rule produces.
Each pixel's color is determined by the color of the three pixels immediately above it (to the left, right, and directly above). At the top of the screen, we see the eight possible combination of three colored and white pixels that determine of the color of the pixel below them.
Note that the combinations that set a pixel to be colored have a 1 above them, and the ones that produce a white pixel have a 0. If the series of 1s and 0s is interpreted as a binary number, it results in a number from 0 to 255, corresponding to the rule number at the bottom of the screen.
Learning Activities
- First, let us start simple. Try generating Rule #2. Notice how a diagonal line forms. This rule says that a pixel should only be colored if the pixel above and to the right is colored and the pixels above and to the left are not. Look closely at a few pixels, some colored and some not, and verify that the rule is working correctly.
- Now let's go with a little more complexity. Try Rule #1. It looks a little more complex despite also following the same eight rules, doesn't it? And now let's go even more complex.
- Try rule 18. Whoa! Things are getting more interesting. Here we have two combinations that work to color a pixel, resulting in a much more complex pattern. This design is interesting because of the repetition of shapes, but very regular and predictable once we get the hang of it.
- Try Rule #30. This rule produces the rich and varied pattern that resembles the shell you saw in the introduction. Dr. Wolfram claims that although many shapes repeat within this pattern, this pattern continues with infinite variation!
- Try more rules. Note that small changes in these simple rules can result in great variation in the pattern formed.
The Next Step
Wolfram contends that these rules are so simple that they can be followed by a "computer" as simple as a single-celled organism. Why not try your hand at it. Go to "Test Yourself" and start replicating the pattern for the rule of your choice. Try multiple rules and see how the pattern emerges.
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