I am running out of things to say. That is normal, 50% of my posts are only pictures. I am falling back into that mode now.

For those who are interested, and for images where the math is visible, I will include some brief code/formula math snippets.

$pixel.value = \sqrt{a}+\sqrt{b}$

The rest of the setup is similar to the previous posts.

The pixel value is a sum of scaled versions of two functions that were used in earlier posts. Specifically, $$pixel.value = 0.5*\sqrt{a^2+b^2} + 4*min(a,b)$$

Another mash-up of functions used for the pixel value $$pixel.value = \min(\sqrt{a^2+b^2},10*\min(a,b))$$

A small variation on the previous. $$pixel.value = \min(0.5*\sqrt{a^2+b^2},4*\min(a,b))$$

The next set of images introduces some symmetry around the diagonal axes in addition to the orthogonal axes.

The pattern in the earlier images could be repeated forever. A vast plane in which wherever you are standing, it looks exactly the same as anywhere else. These new ones, add a unique point at the center. There is an eight pointed star at the center. Other than some small distortion, everywhere else looks like everywhere else.

I am going to dial back on the math. But if you are curious, the additional symmetry is the result of $$z = z^2 /\lvert z \rvert$$ The squaring maps the diagonal axes to the vertical axis. Dividing by the absolute value keeps things the same size.

Feel free to ignore this, but for the curious and so I have at least one line of text: $$pixel.value = a + b$$

$$pixel.value = \sqrt{\sqrt{a}+b}$$

Math for the curious, not required to enjoy the post.

I use a rounded version of the saw function. $$ a = \lvert \sin(x) \rvert\\ b = \lvert \sin(y) \rvert\\ pixel.value = a + b $$