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2011-07-17 Hubert Duprat

2011-07-15 Ashes and ice

2011-07-10 Inverted Julia

2011-06-19 New gigapixel image

2011-06-18 Giuseppe Randazzo

2011-05-24 Gigapixel images are back

2011-05-02 Dan Wills

2011-04-29 Barbara Takenaga

2011-04-13 Play with Ducks

2011-03-31 Karl Blossfeldt

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April 13th 2011

Play with Ducks

I released a public version of the Ducks algorithm for Ultra Fractal. Simply make sure your collection of public formulas is up to date and look for the Ducks formulas in the file sam.ufm. This formula is meant to be used with an "inside" coloring. For instance Statistics in lkm.ucl works well. Use the switch feature with the Mandelbrot-type formula to find nice patterns among the Julia-type fractals.

The version I implemented is a bit more general than the one I described on this blog. One notable extra feature is that it allows to replace the mirror folding by a general dihedral symmetry, what can create somewhat different patterns. For instance the image below uses a dihedral symmetry D2 instead of a simple mirror. You can recognize local D2 symmetries between the groups of four blobs, while regular Ducks patterns only exhibit local mirror symmetries. The difference is more obvious with groups Dn with n large, but I haven't had time to really start exploring them...

A view of a Ducks fractal

20110331-1

In case you don't own Ultra Fractal, Syntopia also implemented the Ducks algorithm in his free fractal program, Fragmentarium. He created a few variations of his own as well.

Works using the Ducks algorithm can be checked here..

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