### Of Doodles and Deformation

## Tuesday, 2004-05-11; 07:55:00

I wonder how many times I can use this title format. :)

If you've had any contact with me over the past year, you'll know that I've really been struggling with these really early morning geo classes. Not only has the time just gotten earlier as the year has progressed (from 9 AM to 8:30 AM), but they've remained pretty uninteresting and just all around annoying because they tend to consume a lot of my time.

Well, the other day in structure class (my current 8:30 AM class), the lecture was a bit boring and repetitive as usual. We were talking about deformation of some sort (since that's basically all we talk about in structure), but I didn't want to go to sleep, so I decided to start doodling. Here's the results of the first page of doodling:

Obviously, there are some notes on there (and you can see the other side shining through, but whatever. Starting from the top of the page, there are the circular and square spirals at the top of the page, the really lame sketch of a physical ball-and-stick model of a certain mineral assemblage, a bunch of small equilateral triangles arranged into a bigger triangle, a similar construction but with a diamond and with everything filled in, a fractal, a funny diagram consisting of mathematical parentheses, and a design composed of progressively bigger and rotated triangles.

I got kind of wrapped up in the last one, so I decided to try and make some more designs in that vein, and got this:

I replicated the triangle design and colored in alternating sections. I also did a similar design with squares and ovals. I actually tried starting with circles, as shown by the other two designs, but they fail for obvious reasons (i.e.: it just turns out to be a bunch of concentric circles, which isn't too interesting). These looked pretty cool, so I decided to continue doing stuff like this. I thought the square one looked better (probably just because the triangular design starts to get distorted), so I drew this:

Cool, huh? I was even complimented on my doodling by a classmate, even though I usually don't doodle much. Bolstered by the success, I decided to redo a triangular spiral design in my OTHER boring class (my linguistics class):

It's not too bad. I think the reason I don't like it is because there are only three spiraling lines, you tend to see the distortion more easily. I also didn't start out the original triangle in the center of the page, so it also makes the design look lopsided.

Currently, I'm working on drawing an even cooler design, made of hexagons instead of triangles or squares. I figured that pentagons would be too hard to attempt just yet (since it's not an easy polygon to draw), so here's the current status of the hexagon spiral design:

I'm actually quite impressed with my work so far on this one because the outer hexagon is still relatively regular, and hasn't become too distorted.

The method of making these "spiral" designs becomes particular evident from this last hexagon spiral. You start with a regular polygon, and then inscribe it in a larger regular polygon that has the same number of sides. The larger ones are ever so slightly rotated one way, so as you progress, you get the various spiraling lines. The number of spiraling lines depends on the number of sides on the original polygon, obviously. Once you start doing it, it becomes relatively easy, as long as you don't distort the larger polygons which is very easy to do unless you step back and look at the overall design. You also have to draw the lines from different directions, so that you make sure you don't propagate a little error throughout one polygon and make it severely distorted.

What's funny is that I'm actually staying awake in class by doing this doodling, so it's probably actually good that I've started doing this. Obviously my attention is still divided, but making these designs doesn't require a lot thinking, so I find that I can easily divide my attention between listening and drawing.

Maybe I'll attempt a pentagon spiral next, or perhaps an octagon spiral. But I'm also trying to think of new geometric designs to draw, because this is really fun to do. :)

Well, the other day in structure class (my current 8:30 AM class), the lecture was a bit boring and repetitive as usual. We were talking about deformation of some sort (since that's basically all we talk about in structure), but I didn't want to go to sleep, so I decided to start doodling. Here's the results of the first page of doodling:

Obviously, there are some notes on there (and you can see the other side shining through, but whatever. Starting from the top of the page, there are the circular and square spirals at the top of the page, the really lame sketch of a physical ball-and-stick model of a certain mineral assemblage, a bunch of small equilateral triangles arranged into a bigger triangle, a similar construction but with a diamond and with everything filled in, a fractal, a funny diagram consisting of mathematical parentheses, and a design composed of progressively bigger and rotated triangles.

I got kind of wrapped up in the last one, so I decided to try and make some more designs in that vein, and got this:

I replicated the triangle design and colored in alternating sections. I also did a similar design with squares and ovals. I actually tried starting with circles, as shown by the other two designs, but they fail for obvious reasons (i.e.: it just turns out to be a bunch of concentric circles, which isn't too interesting). These looked pretty cool, so I decided to continue doing stuff like this. I thought the square one looked better (probably just because the triangular design starts to get distorted), so I drew this:

Cool, huh? I was even complimented on my doodling by a classmate, even though I usually don't doodle much. Bolstered by the success, I decided to redo a triangular spiral design in my OTHER boring class (my linguistics class):

It's not too bad. I think the reason I don't like it is because there are only three spiraling lines, you tend to see the distortion more easily. I also didn't start out the original triangle in the center of the page, so it also makes the design look lopsided.

Currently, I'm working on drawing an even cooler design, made of hexagons instead of triangles or squares. I figured that pentagons would be too hard to attempt just yet (since it's not an easy polygon to draw), so here's the current status of the hexagon spiral design:

I'm actually quite impressed with my work so far on this one because the outer hexagon is still relatively regular, and hasn't become too distorted.

The method of making these "spiral" designs becomes particular evident from this last hexagon spiral. You start with a regular polygon, and then inscribe it in a larger regular polygon that has the same number of sides. The larger ones are ever so slightly rotated one way, so as you progress, you get the various spiraling lines. The number of spiraling lines depends on the number of sides on the original polygon, obviously. Once you start doing it, it becomes relatively easy, as long as you don't distort the larger polygons which is very easy to do unless you step back and look at the overall design. You also have to draw the lines from different directions, so that you make sure you don't propagate a little error throughout one polygon and make it severely distorted.

What's funny is that I'm actually staying awake in class by doing this doodling, so it's probably actually good that I've started doing this. Obviously my attention is still divided, but making these designs doesn't require a lot thinking, so I find that I can easily divide my attention between listening and drawing.

Maybe I'll attempt a pentagon spiral next, or perhaps an octagon spiral. But I'm also trying to think of new geometric designs to draw, because this is really fun to do. :)

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