Spinner Revisited

Here's conceptual way to make spinner from Thursday. Start with this pentagon pattern below. This can be generated by the following polygonR&D code.

start {
  scale 0.4
  create pent
}
pent {
  sides 5
  ifon none {
   paint green
   sides 5
   paint olive
   create pent
   3 right
   create delay
 } { }
}
delay {
  create pent
}

The delay subprogram allows the pattern to development more symmetrically; without it, there would be a radial seam that would break the symmetry (C₅). To add spice to the pattern alternating triangles can be inserted (the zig-zag construction described in Zigzag Grid). To do this, the pent subprogram must be revised like so...

pent {
  sides 3
  ifon none{
    paint olive
  } { }
  sides 5
  ifon none {
    paint green
    sides 3
    left
    paint green
    sides 5
    paint olive
    create pent
    3 right
    create delay
  } { }
}

Finally, some extra triangles are added for decorations to get the original spinner pattern. The colouring of this pattern highlights the triangle- pentagon- triangle groups. It is interesting to see how the colouring has such a dramatic effect for each pattern. A seemingly simple change of switching the green and olive completely ruins the aesthetics of this pattern. The five pointed stars completely dominate instead of being a balanced part of the pattern.

Leaves

The leaves pattern comes directly from the pattern found on Tuesday, August 15, 2006. Here the pentagons are spaced apart by squares. The programming on how and where to insert the squares (really where not to put them) is a little tricky but not overly so. The olive coloured square indicate a filling in square where as the green ones show the growth of the polygons from the centre.

Spinner

This one is a simple pattern that I added a zigzag of triangles.
I'll have to get back to this in a bit--it needs a few pictures to exaplain...

Shells

Maybe tomorrow I'll spiral this one but today I'll stick with concentric rings. The shells made of pentagons are decorated with triangles. The program that made this is not too sophisticated I think that when I try to make a spiral design I'll have to do a little more tinkering.... You'll just have to wait and see.

Heptagon Mix

I was thinking about doing this pattern with heptagons. The problem is that in the old pattern three pentagons fit around a vertex with room to spare but three heptagons do not fit around a vertex. To make room, I inserted two squares and was off to the races. Also, I threw in some triangles to add some variation into the mix. Perhaps this would look a bit more interesting if I added some alternation of colours.... To make an better backdrop, after I cut out the rectangular part that will generate the pattern, I load it into gimp (a linux knockoff of photoshop) and fade the colours (using about a 0.4 alpha on a white background).

Jungle

I'm not sure why I'm calling this a jungle. This pattern is a variant of the one on Tuesday, August 15, 2006. The pattern comes from putting a zig-zag of triangles into every loop in the original. For instance, the original has loops or six pentagons that form a rhombus hole in the middle. Here the rhombus is transformed into curved triangles (the triangle in the middle is just for decoration). On close examination, There are still only two orientations of the pentagons--half the pentagons have a vertical side.

Birds

Perhaps I'm being a bit optimistic that people can see birds. The gaps that are not rhombic (like a diamond) remind me of birds. In the pattern, I see these birds circling around in big spirals. The program that generates this is a very short recursive program. The pentagons alternate between gray and orange. I was a bit surprised at first that there was only alternating colours in the pattern. Even though I programmed the colours to alternate, I am really only programming the polygons to fan in a tree-like fashion. There could be many incidental connections that occur. But on further inspection, all the loops have an even number of polygons so it would be impossible to have two of the same colour. In fact, since each colour represents a particular orientation two pentagon of the same colour can't share just one edge (they would have to share all five or none).