Saturday, October 10, 2015

Opacity Changes

I really like this small change. I wasn't expecting such a big difference. I was aiming to promote the octagram called the Star of Lakshmi or khatam sulayman, which is two overlapping squares following the recent descending pentagons had two overlapping pentagons. I switched back to emphasizing the square rather than the triangles and ended up with this above pattern. I quite like the details in this pattern. Probably, it doesn't actually benefit that much from the animation. Or perhaps I need to work on a different animation...

Descending Squares

Unlike normal, I was able to deliver the square version of the descending pentagons quickly. There was no math to figure out. although there was one interesting choice that I looked into. The choice was to place the 45 triangles to be touching the previous square rather than the corner square. I guess it's simply a preference about complexity. I like both.

The first version is a simple analogue of the descending pentagons--actually it was the original doodle on my boogie board. I find the boogie board is a great exploratory tool because of it's impermanence. Somehow it helps me focus on process rather than product. The version of the boogie board I have doesn't save any of your work and there is no erase so you are stuck with any mistakes unless you erase the entire drawing. So I am tasked with focusing on the internalizing any thing that I do that I think is important. Perhaps this is a bit of a throw back to all the time I spent with chalk and blackboards. Regardless of the tools, the square doodle is a decorated version of drawing a square then using the midpoints of the square as a new square. The corners of the original square then get decorated with their own squares. The second version of this descending square alters the importance of the decorations by using them as a key functioning part. The decorative triangles determine the scale of another layer--it has to fit in the previous square.

I'll look at variations for the pentagon.

My intuition tells me that the hexagon won't be as interesting but I'll probably check it out anyway. If there is anything of note I'll post it.

Descending Pentagon

 You have to reload this page to see the animation ...perhaps I should put it on a bit of a repeat.  It took a surprising amount of high school math to unravel how to make this.  I guess I could have been content with just eyeballing it but that seems to take all the challenge away plus it makes it more difficult to augment later. Perhaps I should have used a better tool than Excel: maybe Geometer's Sketchpad.  Next time.  Perhaps I'll put up the square version of this pattern when I get the time.  
Essentially, it's a snazzy version of starting with a pentagon and using the sides midpoints to make a slightly smaller pentagon and descending forever (or in this case 12 levels?).  The snazziness is was the time consuming part.  Computing the lighter bands took a bit of effort--more of a stamina thing rather than a difficult thing.

Saturday, March 07, 2015

Octagonal flowers

This pattern has a few cute things: a right and left handed version of the flower and some structures that seem a little out of place. The green flower is the left and the purple is the right. What I find more interesting is the way the 4 octagons behave between the flowers--there is a diagonal slit between them that alternates its direction.  The pentagons are just decorative but they make the white space more interesting.

Sunday, March 01, 2015

Quilt and wallpaper

I was going to try to get this into last month but alas February only has 28 days this year. here is a toned down copy that works for wallpaper wall (colour), wall (blue), and wall (sepia). I was a bit lazy using a tool to crop it so it's in pdf rather than svg...but my MacBook pro accepts it as my desktop background so I didn't pursue it.

Sunday, February 01, 2015

from Pentagons to Heptagons

I needed to do a modification to go from pentagons to heptagons: add a square between the triangles. Without the square the heptagons would intersect. I wonder how close there pentagons are....

Monday, January 26, 2015

Elegant pairs

I was experimenting with the pervious post's pattern and the particular twist I was attempt wasn't fruitful but I did end up with this pattern. There two key pairs in this pattern: two purple rhombi (made with triangles) and the prominent pink/purple triangle-pentagons. I call this pattern elegant because of its fine lines: the slim dart gap between the rhombi, and the near touching pink polygons. Perhaps these fine features are also amplified by this type of symmetry.
I may have to augment my tool to help play with the colour choice and perhaps add in an easy centering tool. I guess these are less of a priority just a little of an annoyance...
Here are some png wallpapers

Sunday, January 25, 2015

Nice 6-fold symmetry

I like this one. Essentially, it's variations on a theme. Perhaps I add a twist and see if it will be as pretty.

On a side issue, didn't work when I put https which redirects to which needs the https. Not surprising but there certainly is a lot of details to juggle--at least when you are doing posting content on the cheap... Of course, if Blogger simply let me upload my svg files I wouldn't have to do any gymnastics...

Sunday, January 18, 2015

Pentagons and Triangles

Here's a new pattern.  I have been a bit too busy to post this last semester.  Hopefully, next semester I'll have a bit more time to play with patterns.  This one has a few variations that I may continue to play with...  

Saturday, September 13, 2014

Tileland+ code

Tileland+ interface
Along with an interface update, I added a some language extras.  The native Tileland instructions remain (polygons, colours, and turning) but now I have added the environment instructions to the language.  In particular, I have added clipboard manipulation instructions. Although somewhat hidden, this addition is a metalanguage or a preprocessing language.

It's actually pretty simple when you see an example.  An orange hexagon with a blue square would be 6 o 4 b.  The picture below is a that with a right turn or 6o4b>.  The colour follows the shape so that it has something to colour. Doing that 4 times is just 6o4b>6o4b>6o4b>6o4b>.  Another way to make the pattern is to use the clipboard.  I haven't yet introduced a concept of a cursor yet so the clips come from the entire current code. There are 5 instructions that affect the clipboard: x, v, n, m, and q.  The first, x, simply transfers the current code into the clipboard.  The second, v, adds the first clip to the current code. The next two n and m roll the clips left and right. The final one, q, clears all the clips.  The other letter instruction, z, removes the last chunk from the current code (only really useful in an immediate situation).  So, to make the loop of squares and hexagons using the clipboard you could type 6o4b>xvvvv or cut and paste that into the code textbox. The result of either action is [6o4b>][6o4b>][6o4b>][6o4b>] -- the brackets chunk the code but do not affect the resulting picture.

The code in the Tileland+ image was produced by using 2 different clips -- this required using the n and m instructs to change the first clip back and forth.  For instance, in this code, "6o4>6p>>>4o>x 6o4>x  vvvnvmvnvmvnvv", the first two chunks make the clips and the third chunk use the two clips.  In terms of cutting and pasting sometimes it's best to start with a fresh clipboard so an initial q can make a fresh start -- so q6o4>6p>>>4o>x6o4>xvvvnvmvnvmvnvvmvnvvmvnvvv so  makes the pattern in the image.

Play around with this version of Tileland and tell me what you think.