### Illusional Artistry

May Cuties posted a really cool optical illusion today. I had almost forgotten how much I love these kind of things. Here is a web site with lots more. They're all pretty good, but my favorites are #13, 29, 36, and 38. By the way, if anyone can figure out the answer to #38, please let me know; it's driving me crazy!

Several of these, particularly #2, 8, and 25, are based on the paintings of the brilliant Dutch artist, M C Escher. My dad taught me to appreciate Escher's brilliance when I was barely old enough to read, and while my once-childlike sense of wonder may be a bit world-weary these days, I'm still stunned and awed all over again whenever I revisit his magnificent work.

My friend Soccer Dad enjoys posting fractals now and then. Some of Escher's work reminds me of those computer-generated images; it never ceases to amaze me that a mere human being was able to achieve such heights of imagination and such visual and manual precision, working in a pre-computer world with humble paints and ink. Peruse the web site link above when you have a few moments, and see what I mean.

## 4 Comments:

Elie, I think that if you look closely you'll see that the angle is a bit different on the two figures. They look similar enough, but the angle is steeper in one of them and perhaps accumulates the area of one square? Take a look and see what you think.

OK, I "did the math" and I think I figured it out! If you calculate the areas (in grid squares) of each of the four figures and of the big triangle formed by them, you get:

Red triangle: 3 * 8 / 2 = 12

Dark green triangle: 2 * 5 / 2 = 5

Orange shape: 7 squares

Light green shape: 8 squares

So the total area of the four individual shapes is 12 + 5 + 7 + 8 =

32. But the large triangle formed by the four shapes appears to be 13 by 5 grid squares, so it's area should be 13 * 5 / 2 =32.5.Thus, there is 1/2 square worth of leeway, and therefore there must be some fudging between the exact sizes of the shapes in each picture, as SS points out above. They must be slightly bigger in picture 1 and slightly smaller in picture 2, accounting for the 1 square total difference.

Not obvious to the eye though!

#40 (http://www.123opticalillusions.com/opt40.htm) for me was the winner. I had to use Apple's DigitalColor Meter to believe what I saw.

I thought #40 was an error! Even if I cover up all the other squares and just look at those two they still look like totally different shades. Amazing.

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