Jazzing up old designs

I'm playing around with gimp (a photoshop-like tool) to add some fullness to my designs.  It's nice to have a better selection of colours and gradients. With the broccoli picture above, I like the way the curves lines contrast the hard edges of the pentagons. I need to update PolygonRnD to give me higher resolution on the small pentagons. Originally when I made the software, I did not allow for changing scale so there was no need to output more than 3 decimal places for the coordinates...now I have to go back and fix it.  I'll get around to it eventually.

Here, I just played with gradients and shading outside the pattern. I like the warm colours as well as the blending of the types of pentagons.  I posted paper versions of this in my office with the hopes of capturing some young minds in the patterns.

2 balloon decorative truncated tetrahedron

I've been playing around with a few balloon patterns that have odd degree vertices.  Lately, I revisited the doubling up the edges approach.  Here's my latest pattern.  The notation is a bit cryptic but. The pink strokes indicate where a connection has to be made. The big numbers mean  big bubbles and the small numbers mean 1 inch bubbles.

Probably this would make an OK flower vase--it has three points of contact which is good for balance. This is a view from the top. I'll probably make a youtube vid on this.

more flowers

Here's a simple pattern made with a 3 pentagon 2 square spacers.  Take away the spacers and you end up with a very dull triangular grid.  Since there is so much white space the bright colours seem to work without being over powering.

another bug

This pattern is a bit of a revisit of X bug from Jan 2008. I like the chevrons and the gear like aspect. Does seem a bit spread out though.  I'll play some more to see if there is something worth looking at.

Squared Triangle...

I liked this quote.


“Jokes of the proper kind, properly told, can do more to enlighten questions of politics, philosophy, and literature than any number of dull arguments.” 
― Isaac Asimov


I tried to come up with a polygon joke but this is the best I could come up with.  I guess I should stick with dull arguments.



It's not any funnier going the other way...

updated PentTree

After the starfish design, I revisited the PentTree. The first thing I noticed was that it didn't make all the nice loops--connected rings of polygons. So I fixed that: check above the base, you should see eight pentagons that fit together making a loop.  Then I tweaked the pattern so it was a little better balanced. For the geeks, here's the code:

splitL{    right    scale 0.71925    right    ifsmall 0.002 { } {    sides 5    ifon none {       paint green       left       create splitL       right       create splitR    } { }    } }

splitR{    scale 0.71925    ifsmall 0.002 {} {    sides 5    ifon none {       paint olive       create splitR       left       create splitL    } { }   } }

StarFish

This is a fun image that has a lot of pentagons and isosceles triangles. This pattern has neighbouring pentagons having the ratio of the .618 (the golden ratio). I'll do some more exploring to see if I can find another interesting pattern.

I think this may overly complicate the pattern but here is another.  Maybe this is more like an amoeba. It was a little tricky to make that inner spiral fit but it does.

 

Koch snowflake variant

This one was fun to make. I wanted a cool snowflake to be a backdrop for a presentation (http://prezi.com/jie04ey9bhjr/zulo/) that I was making but I couldn't find one that I liked.  So I figured that I would make one with PolygonR&D.  After som playing around, I ended up with this one that I later enhanced with some photoshop (gimp actually).
Let me know what you think.

The Spins

Nonagons and triangle seem ripe with possibilities for making repeating patterns.  I'm going to have to begin a catalog of my patterns so that I don't recreate too many.

Lots of legs

I guess I have too much time on my hands. I'm playing with the idea of having 1.5 turns clockwise mixed with a half turn counter-clockwise. Perhaps I should work with 2.5 and 1.5 mixes... Must get back to Tileland...

Heptagonal flower

I was playing around with TileLand and I stumbled on some local patterns that I turned into this picture. It seems to suggest a lot of lines and make it hard to decide what you should focus on: flowers, rounded triangles (Reuleaux triangle), or triplets of arrow heads. 
     The way I generate the pattern is by connected paths heptagons an triangles.  I'll take a step back and see if I can come up with some ideas about this pattern.    With a regular polygon focus I have ways of describing the connection between the two types of loops and simpler patterns....  I'll keep you posted.
    This extra colour makes it a little more interesting perhaps...

Fibonacci Fern

I wrote a short story about this fern to try to motivate the formula to the left.  The geometry of the fern directly relates to rectangles with lengths that are Fibonacci numbers.

This square, 55x55 is composed of the following rectangles 1x1, 1x2, 2x3, 3x5, 5x8, 8x13, 13x21, 21x34, and 34x55.  Then, I take each of fold each of the rectangles in half to create the fern.  It's an interesting shape that has a different front and back.
The story is called Symposium and is still a work in progress.