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.

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.

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.

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....

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

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, tinyurl.com/p3c6mdh/newPentTri2.svg didn't work when I put https which redirects to https://c3b8f482385fc05f71d246e2e23a26cb99a3c770.googledrive.com/host/0BwD1YaggiIIAY1gxNEJEa2JKNlU/newPentTri2.svg 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... I ended haven't to use my own host.

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...