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Showing posts from October, 2006

Decagon Web

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A web of decagons woven with pentagons. The holes are irregular hexagons made from two overlapping pentagons. Perhaps I should have made the green pentagons pink but sometimes it's hard to say no to green. The pattern derived from the Degagon Zig-Zag: using pentagons instead of triangles and filling in a bunch more pentagons. The rotation symmetry of the purple pentagons is a remnant of the zig-zag construction.

Decagon Zig-Zag

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This is a variation on the last pattern. Perhaps I needed to have a colour upgrade. Maybe tomorrow I'll try for the same repeating structures on the outside but with the same central loop as the last pattern. The zig-zag part of the title refers to the triangles that are inserted between the decagons--the first go right then left.

Decagonal Flower

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This decagonal flower is based on the pattern from August 8th (which uses nonagons--nine sided polygons instead of ten). The decagons are arranged in a back and forth loop and then the triangles were inserted in a zig-zag pattern to form the inner loop. The rest of the pattern, the outside, was added as decoration. Notice that there is a bit of conflict of rotation. It seems that the ten gaps seem to infuse a of a counter spin into normal spin of the inner loop.

Shrinking Pentagons

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This star shape is constructed primarily with blue pentagons that are only touching at one point with another blue pentagon. The blue pentagons are shrinking by a half each step to the away from the centre. The purple wedges fill in the gaps between the blue pentagons. The wedges are constructed in the same way--pentagons that shrink by a half. I'm still playing around to make a better looking pattern with pentagons of different scales...

Flowers

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This pattern of flowers is generated by introducing a zig-zag of pentagons into a grid of hexagons and triangles. zig {
sides 5
paint purple
sides 3
ifon none {
paint green
3 {
create zag
right
}
} { }
}
zag {
sides 5
paint purple
left
sides 6
ifon none {
paint yellow
6 {
create zig
right
}
} {}
}
Instead of the program, the pattern can generated like the windmill pattern. Below, we have the elaboration of a hexagon/triangle pair to a the pair with a pentagon inserted between them. As with the windmills, the orientation or the elaboration is important.

A Field of Windmills

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This pattern is a variation of "Not the Zipper". The main difference is that the pentagons have sides half the length of the triangles. They share only one vertex now. The negative space of a single loop reminds me of a windmill--hence the title.

A way to understand the generation of this image is to start with a triangular checker board of orange and purple then elaborate it using the following visual replacement rule.

Pentagon Play

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This pattern is the same as the purple and blue pattern from August the 15th. The twist is that the edges don't line up. The holes that used to rhombic holes now look like odd candle sticks. The program is almost identical to the Pythagorean tiling except the "sides 4" is replaced with a "sides 5"(as well the loop must go fives times rather than four).

Fractal Pentagons

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This pattern is a fun pattern with pentagons. Each step away from the central pentagon the adjacent pentagons get smaller. Here is the code that describes this trait.go{
scale 0.5
right
scale .6180339887
right
scale 2
sides 5
ifon none {
paint purple
5 {
create go
right }
} { }
} To highlight the layers of pentagons I alternated the colours.