Circle Packings with Linear Fractional Transformations

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A linear fractional transformation of the complex plane has the form , where , , , and are complex, and . Such a map is conformal (i.e. it preserves angles locally) and preserves generalized circles (i.e. lines or circles map into lines or circles).

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The transformation here acts on a hexagonal grid with disks inscribed in each cell. Mapping just three points, it is possible to calculate the radius and the coordinates of the centers of the new disks.

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Contributed by: Enrique Zeleny (January 2015)
Open content licensed under CC BY-NC-SA


Snapshots


Details

Snapshot 1 shows the hexagonal grid with disks.



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