Perception of Difficulty: Change Colors

Disclaimer: this post is opinion based.

A few years ago, I have tried to write a JS code to draw some fractals. However, I was not able to come up with an original and beautiful result. So, I have modified the code a little and made it draw a bunch of lines with random colors (and repeat that every second.) You can view it here.

Back then, I did not see anything particularly nice about it but after a couple of years, when I look at it again, it makes me think about our perception of difficulty. Let me emphasize that it draws exactly the same lines at every run, it is just the colors that are random (unless, of course, I have made an error.) So, in theory, no matter which set of colors you start with, if you diligently trace the lines, you can understand the pattern of the lines. Here is a sample picture:

image1I do not know about you but the above picture does not give me a lot of hints about its pattern other than a possible point of symmetry. So, I would say that it is hard to recognize a pattern, if it exists at all.

However, if you change the colors a little bit, a spiral in the middle becomes clearly visible.image2 (Click on the image to see a bigger version.)

Tweaking a little bit more, we also getimage3which makes it more clear that these lines are polygonal chains approximating some circle-like path. Well, it is an approximation of a spiral.

As you saw, it became a lot easier to notice a pattern when you change the way you look at the lines. A quite similar situation happens often in my daily life; when I spend a lot of hours working on a seemingly hard mathematical problem, only to realize that I have been using wrong “colors”. Of course, in general, you do not know which “colors” to start with but if you find something challenging, it is often rewarding to change “colors”.