Rosettes from Photos

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This Demonstration gives some examples of rosettes produced from photos. You can choose aspects of shape and symmetry with the functions and , with the complex parameters and , defined in the Details.

Contributed by: Izidor Hafner (March 2016)
Using work by: F. A. Farris
Open content licensed under CC BY-NC-SA


Snapshots


Details

The following results are valid:

If, in the sum , unless , is a rosette function with -fold symmetry.

If, in the sum , unless , is a rosette function with -fold symmetry.

If, in the sum , , is a function with mirror symmetry.

The functions (cyclic) and (dihedral) are defined by and .

Reference

[1] F. A. Farris, Creating Symmetry: The Artful Mathematics of Wallpaper Patterns, Princeton: Princeton University Press, 2015 pp. 40–45.



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