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Showing posts from November, 2006

Tri-triangles

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Three different triangles fitting nicely together. This one came directly out of the wonderful book Tilings and Patterns (p. 74). There are a few ones similar to this one as well that I may put up there. I'm more a fan of the patterns that come from polygon loops that are combined rather than ones like this. Still these ones are easily described since they have only one local neighbourhood. The PolygonR&D program has only one subprogram that describes the path from a purple triangle it's neighbour. The smallest triangles are not drawn since they are white.
tri {
right
scale 0.625
left
sides 3
paint orange
scale 1.6
sides 3
ifon none {
paint purple
3 { create tri
left
}
} {}
}

A New Checker Board

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This one has a lot of patterns in it. At some vertices you can see three differently coloured teardrop shapes that form a propeller. In fact, each teardrop shape belongs to only one propeller. The pattern can be thought of as a particular colouring of a hexagonal grid where certain hexagons are broken into six triangles. Let me know if you want to see more patterns like this one.

Eggplant

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Well this one is simply labeled eggplant because of the colours. The pattern demonstrates some local three-way rotational symmetry and some local three-way reflectional symmetry. The program that created it only has two sub-programs: one that describes the neighbourhood of nonagon with four triangles around it and another one that describes the neighbourhood of the nonagon with only three triangles around it. Those are the only local neighbourhoods in the pattern.

Non Play

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I'm still playing with nonagons. I'd like to have PolygonR&D create a similar pattern to this one but I'd like it to be a be less regular. Right now when I extend, I end up with six wedges that look too regular and have too many three point stars. I'll keep up the non playing until I get a pattern that has pattern and not too many three point stars. I hope to make some non sense soon.

More Cats

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Here is the promised dancing cats with colours that highlight the spiral nature. Close to the edge it becomes easier to see the straight edges which form an overall polygonal nature of the pattern. Unfortunately, I achieved this pattern by triplicating the original code that generated the pattern. On further reflection I may try to rewrite this another way so that this cutting and pasting isn't required...

Slippery Triangles

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These triangles have slipped a bit. They used to be all lined up then they started to slip. Now they have these gaping hexagonal holes. This pattern is related to the pattern called Pythagorean Tiling where the same thing happened to squares. The big Squares slipped and made little square holes. I wonder why I ended up choosing the same colour. I get the feeling the more of these patterns I make I'll end up repeating some days and not even know it.

Dancing Fat Cats

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Perhaps I should call this dancing cat slugs. I'd be happy to entertain some alternative names for this one. A close examination of this pattern may reveal a connection to the spiral with nonagons. Notice the same three interconnected spirals appear here--different colouring would help see the spirals but I think it would destroy any catness that the pattern has (slug or otherwise)...

Wings

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Busy times call for quick and dirty variations. This one is entitled wings for the shape of the gaps on one side of the gray squares. It comes from a variation of a simple pentagon pattern. A zig-zag of squares is inserted into the simple pattern. Half of the squares are not visible but the ninety degree angles can be seen from in each wing. Perhaps I'll have to revisit the way program deals with colour so that I can have more choices....

Dodecagon Elaboration

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Here we have octagons and triangles making up the majority of the pattern. The blue hexagons just fill in the centres of the patterns. The pattern comes from combining a number of discs like the one found in sun-spot. At a larger scale the discs can be thought of as dodecagons and the large triangular shaped that have six point triangles in them can thought as triangles. With just the dodecagons and triangles we are left with a simple pattern where there are no gaps and the vertices are all the same: two decagons and one triangle. The orange and purple of the octagons makes it more difficult to see the elaboration especially since the discs eight-way symmetry is highlighted not the twelve-way symmetry.