The simplest case is one where the size of the Stabile is evenly
divisible by the size of the Mobile. In this case, the path
drawn by the pen simply repeats the same trip around the Stabile
every time, as shown in the figure below right.
In the figure shown at right, the
radius of the Stabile is 200, and that of the Mobile is 50.
Therefore, the perimeter of the Stabile is exactly 4 times that of the
Mobile. This combination yields a spirograph figure where the
path drawn by the pen has 4 parts or lobes, corresponding to four
complete rotations of the Mobile.
Now, more complicated figures will appear when the size of the Stabile is not an integer multiple of the size of the Mobile. This all falls out of the prime factorization of the sizes. For example, let's say we chose a Stabile size of 150, and a Mobile size of 70. To predict the maximum number of points or lobes that a spirograph drawing will have for those two sizes, we need to divide the Stabile size by the least common denominator of the two sizes.
So, if you want a figure with a certain number of rounds N, choose a Stabile size as an integer M * N. Then, choose a Mobile size M * P for some value P, such that M and P are mutually prime. For example, if we wanted a figure with figure with 21 lobes, we would follow the procedure like this:
This kind of design process lets you predictably put together really nice pictures. Click on the excerpt at right to see a two-part drawing that was made with a Stabile size of 105.
 
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This applet and accompanying back-end web system were written by Neal Ziring, last modified 6/5/00.