Subtle pentagons

I was playing around with some slippery pentagons and ended up with this pattern. I was trying to get them to squeeze together a little better and was having a bit of difficulty. I didn't look carefully enough to see that the gaps were very different. I was focusing on the lines of pentagons and I missed that the gaps changed half way along the line. It's interesting how the regularity can fool you into thinking that it's more regular than it is. Perhaps it's not that subtle and I was just playing after a long day of work.

Playing with Slippery Triangles

It's been a while since I have posted a pattern. I guess it's been busy. I modified Slippery Triangles to make this. The original purple triangles were replaced with limited Sierpinski's triangles I'll include the first couple of iterations. I put red triangles as the initial triangles so that it would be clearer what the progression was. I made sure that the purple triangles didn't get too small otherwise they would be difficult to see.

One of the things that I find appealing about this pattern is the slightly out of alignment of the triangles. It introduces a bit of conflict into the pattern. As well, by stopping the replacement of triangles at a coarse level I think that it suggests the a fractal pattern but stops short. Perhaps I'm over thinking this one.

Zigging with Heptagons

Today's quickie is a variation of Zigging. I put heptagons in and was required to add a few more polygons to make them all fit together. Without the squares and the triangles, the heptagons would overlap with each other.

The outline of the gaps reminds me of ducks. To help make that more visible I need to use better colours. Perhaps, I'll have to update PolygonR&D to have more colours. Then again I guess post-editing in photoshop or gimp could easily fix this.... If that is the case, I guess I'll have to have an option to not use anti-aliasing so it is easier to swap colours... The work of a programmer is never done.

Zigging

Here is a quick little pattern with the triangular grid only partially expanded. The diamond shapes are two triangles that did not have a spacer inserted. These last week have all been variations on a theme. I'm sure I'll switch themes soon. Perhaps I'll start introducing a few of my concrete constructions....

Hour glasses and Pythagoras

There's lot's to see in this pattern. The idea was to elaborate a square grid using triangles. By using larger triangles, the pattern creates a number of interesting features to focus on.

The first features are white hour glasses made with the two white 120 degree isosceles triangles. They have two orientations that alternate. These are the holes that come from the vertices of the original square grid. The size of the orange triangles was selected to have the triangles share a vertex. A smaller size of triangle would leave a gap which could be seen as the white isosceles triangles overlapping.

The second features are large squares that are defined by a purple square and it's four neighbouring equilateral triangles. This square that also be identified as a propeller can be chunked together with similar squares of the same orientations to create a tiling that is a Pythagorean tiling. What is interesting is either orientation of a purple square can be the basis for big squares and that each produce a Pythagorean tiling. It really is just a mater of switching your point of view and chunking different polygons together.

Little squares and big squares

Today I'm playing with size a bit. I have two patterns that seem a lot different but only differ by the size of the squares used. As with my recent trend of elaborating a triangular grid by inserting polygon sequences between the triangles, here we have a triangle-square-triangle being inserted. By changing the size of the square inserted the squares can be made to meet in the middle of the hole produced by the insertion.

The change in the amount of white space and the addition of the pointy features makes the pattern feel a lot different even though they are closely related.

To highlight the path of the insertions and the role of the original triangles, I have included close-ups showing the path of the new loops.

Another Triangular Grid Variation

This pattern uses the same strategy as the last one. In this case, the inserted polygons are a square, a pentagon and a triangle. There seems to a little too much going on to be attractive. The holes in the pattern are reminiscent of the shurikens. If you look back at that pattern it is pretty much the same except the inserted pattern does not include a square. The three different shapes of holes are analogous.