Thanks to everyone who viewed or commented on my images, Mom and Dad. Several people asked how I did them, so here's a brief description.

I created them both in Ultra Fractal. I did Mom first and it's based on the Hilbert curve. The Hilbert curve is a fractal curve that is based on breaking up a square into a 2x2 grid of squares, breaking those up into smaller squares, etc., and drawing a curve through the centers of all those small squaes. I wrote an auxiliary program to generate the coordinates of the corners points of the curve and write them to an Ultra Fractal coloring formula. Then, I took the grayscale version of my mom's picture and reduced its resolution to an appropriate level. Then, I wrote another auxiliary program to interrogate the photo and write the grayscale levels to the coloring formula. When Ultra Fractal rendered a pixel, the formula determined the grayscale level of the spot in the photograph that corresponded to the pixel and used this to adjust the thickness of the segment of the Hilbert curve that was closest to the pixel. The Hilbert curve was thus rendered as a black line of varying width on a white background, similar to this example. The actual Mom image is made up of three layers, each with a permuted photo and Hilbert curve, combined using the "difference" merge mode. The result is a continuous curve which resembles the Hilbert curve, but is slightly different from it, and a series of discrete dots.

The Dad image was created in a similar fashion. A major difference is that I used two different curves, both based on a 3x3 grid instead of the 2x2 grid of the Hilbert curve. Here is a sample of a layer from that image.

Thanks for your interest in my work!

Kerry
www.fractalus.com/kerry