I had always known the beauty and power of mathematics, but after discovering the connection between complex numbers and fractals, I became deeply fascinated in how fractals express and reflect that beauty. Whereas mathematical beauty often lay in abstract concepts and elegant proofs, fractals bring the beauty of mathematics plainly to the surface, unobscured and for all to see. Following my curiosity, I wrote a Java program to generate and explore fractals, as I find that creation and experimentation often brings about a deeper sense of understanding than just observation. At the time I had just tackled a number theory problem regarding tetration (super-exponential functions), and decided to generate fractals based on that. After generating the fractal, I experimented with changing my rendering method a little bit, and to my surprise, a completely new form of fractals emerged, which is shared here. The base function for all these images is still simply standard tetration, the only difference being that color (or shade) of each pixel (representing a point in the complex plane) is dependent on the maximum reference angle of that point as tetration is repeatedly applied, rather than whether or not the magnitude of that point would increase without bounds, the latter being what standard tetration fractals are made from. I was astonished that such a small change would produce such intricate results that were quite different from normal tetration fractals. No matter how much I think about it, I am still amazed that the basis of these images is purely mathematics, and I hope to share that beauty here in this gallery.

— *Stephen Ren, North Hollywood, CA *

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