# Number Systems Using a Complex Base

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The points are the set , which is the approximation of the fractional parts of all the numbers in the base system with digits, , . (Integer parts () are suppressed because the result would be almost the same.)

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Contributed by: Jarek Duda (March 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

For more information on the theory behind this Demonstration, see:

http://xxx.arxiv.org/pdf/0712.1309

The width function and the equation for the center of symmetry are restricted to a finite number of levels for better appearance, but the length of the circumference and the area of the convex hull are calculated for the full convex hull.

The method of calculating analytically the Hausdorff dimension of the boundary using recurrence is explained in:

http://demonstrations.wolfram.com/TheBoundaryOfPeriodicIteratedFunctionSystems

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