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I just started my investigations about tesselations and tilings for some very special kind of design Project. I came over that image:

Giant Pufferfish Skin Pattern

It shows a part of the Giant Pufferfish's skin and I am very curious about to find out how this pattern could be generated, so that it can be continued infinite in x- and y-direction, without self-repeating.

However I am not a mathematician and quite new to this Topic, so I appreciate any Kind of Help or Hint that gives me some guidance.

Thanks in ahead!

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While this isn't quite the same (your pattern has plenty of the yellow pieces disconnected from the main group), you might consider the example on the Wikipedia page. If you could implement or find blur/sharpen algorithms on a torus (i.e, they act as if the edges of the image are connected to each other pac-man style) then the result should automatically be a tessellation. I think the major issue would be actually generating the pattern itself. – Robert Mastragostino May 2 '13 at 6:10
You should watch this. – Raskolnikov May 2 '13 at 6:37
@Raskolnikov I watched the video and searched along for Turing patterns, because that is indeed a very good approach, nearly exactly what I am looking for. Do you probably have some more resources for that? – philipp May 2 '13 at 13:48
You could start with the original paper of Turing and maybe look up the papers of professor Philip Maini. – Raskolnikov May 3 '13 at 5:39
@Raskolnikov Thanks for that, I will have a look at it. – philipp May 3 '13 at 5:56

The first mathematician I know to tackle the problem of pattern formation in chemical processes and biological morphogenesis was Alan Turing in his seminal paper "The Chemical Basis of Morphogenesis". As you'll notice, it is not quite what you had in mind. But if you delve into it more deeply you might find things analogous to tesselations. I just doubt that tesselations are really the way to go when describing this type of patterns.

Here's a nice video lecture by professor Philip Maini about that topic.

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