Rhombuses self similarity

 

Everyone likes fractals don’t they? I thought it would be fun to make one up with rhombuses (I like rhombuses).  So here are some things I’ve been playing with.

3 rhombuses

I started with 3 rhombuses made of two equilateral triangles which shared one vertex. Drew another rhombus with its longest diagonal the same length as the shorter diagonal of the first in each. Then used a vertex from the original rhombus to crate a smaller rhombus connected to a vertex from the second rhombus.

OK that doesn’t sound like it makes much sense. Regardless, we have two types of rhombuses, filled and unfilled. If the rhombus is filled it grows an unfilled rhombus from one vertex of its shorter diagonal, and two filled rhombuses on either side equal in size to the filled rhombus. If the rhombus is unfilled, it grows a filled rhombus across its shorter diagonal. Unfilled rhombuses can overlap, filled rhombuses cannot.

Once I have these rules I can play around with what they do and whether the pattern is a fractal or not.

So I did a few drawings on paper, a couple of paintings, drew some on the computer and had a good play around. It was also a nice opportunity to explore techniques and colour interatction, texture and surface of paint and creating noise in digital images using the original drawings.

I’ve not finished with this yet, from one picture you might think you know where the pattern will develop to, but then another picture might contradict that. So why not keep playing around eh? It’s like a walk into a rhombus shaped woodland, you don’t know what funny little plants and mushrooms are growing round the corner.

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converging rhombuses

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