Monday, April 12, 2010

Spatial Reasoning Games and 3D Binary Phrases

I started using this method of doodling in class in high school, and I've kept at it (and some minor variants) since. I was thinking of creating a step by step guide, but the whole fun is working out how to do it, so I'll try to find a middle ground on the whole ambiguity front.

The basic premise is as follows: Get tired of paying 100% attention to your professor, and decide to doodle. Then think of a short (maybe 3 word) phrase. I'll use "one two four" as a suitable example. Convert each of the letters in the phrase to the binary equivalent of their numerical place in the alphabet (a = 1 (decimal) = 1 (binary); b = 2 (decimal) = 10 (binary); c=3=11; d=4=100; et cetera). Now use black squares to represent 1 and white for 0, and create a grid for each word with the letter on one axis and the binary place values on the other, like this:
In reality, do this step in your head and go straight to the next one, but for the sake of explaining, it had to be diagramed.

Now, take the first word and draw it in on the x-y plane. I use one square on the diagonal per two squares on the horizontal. Like this:


Expand it into cubes:

And then do the same thing with the other words and stack them:

All that is easy once you get the hang of it. The next step is to mentally rotate the figure ninety degrees and draw it over from that angle. And then rotate it again. And then again. My notes end up looking like the left side of this page. I added the letters and numbers for your convenience. 

(Click to enlarge)


When I get tired of this, I mix things up and add more complications - my current favorite, as seen on the right side of the page, is assigning a binary place value to each side of each cube, and then writing another word or phrase across the blocks of the original words. You can see that I cheated a little for the second part and drew "floor plans" of each level before I drew it. All the insides are really tricky to keep track of. But on the left side I didn't cheat at all; I drew it straight through, only making minor changes for poorly drawn lines.

It's fun. I recommend you try it.

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