Figuring Out Affine Transformations: Frustrating But Doable

[srn]

I need to determine the affine transformations used to produce the following image:

Been staring at it for an hour and it's frustrating me to no end because it's probably really easy. Clearly it gets scaled by 1/3 and there are 3 linear transformations that put it at (0,0), (1/3,1/3) and (2/3,0) but I don't know how to produce the vertical edges. It's not iterating anything, it's just a line that keeps getting bigger... Take the original image, remove the y-coordinates, scale by 1/3 and rotate, or something?

 

[micromass]

Yes, try some kind of projection on the x-axis.

 

[srn]

Got it. Thanks, guess I just needed a little push in the back. :)

 

[HallsofIvy]

It's clear that the basic transformation is something like
f(x)= 0 if 0< x< 1/3
f(x)= 1 if 1/3< x< 2/3
f(x)= 0 if 2/3< x< 1.