It is the mathematics behind the art that holds the greatest fascination for me. But the images, unlike the math, can be seen and as visual representations of arcane numeric manipulation, they are fascinating to look at. More fascinating for most people than the formula at the image's heart.
This art may have been what I was looking for in high school when I did a science project attempting to graphically display functions using imaginary numbers as variables. Fractals didn't exist back then although some related concepts were known about very few people were aware of them including me.
The project didn't get much traction primarily due to the low-tech limitations of the slide rule (my only calculating device) which had no capability of calculating imaginary numbers) and the mountains of iterative calculations that needed to be done even for a sketchy outline. Despite its inadequacies I still have that slide rule within easy reach.
Then, in 1986 I had a computer. I wrote my own program for creating fractals but again technology was a limiting factor, at least as far as creating beautiful images was concerned. The images were primitive given that the typical "advanced" computer graphics cards of the time allowed for only 16 distinct colors. By way of comparison, I am currently using a printer that uses 10 different-colored ink cartridges, the better to blend the millions of colors available with today's computer graphics cards.
The art created through mathematics can be startlingly complex or elegantly simple and beautiful.