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The file doodler_v5.py, available below, contains python code to simulate the interesting designs created by the simple LEGO EV3 Doodler .

There are comments in the file that should help explain how the calculations are done.

Here's a picture of the Doodler and some designs made from it (taken from Breberky's builder page):

Below are simulations of designs from the python program; these two simulate the cases shown in the WMV demo video on the LEGO page.

(There are some differences which may be due to the "slop" in the Lego structure introducing hysteresis?)

Using other parameters (11 to 7 ratio):