The Wonder of Newton | A Special Fractal

It certainly resembles an abstract image. Pulling one in different directions. Screaming.

Talking rapidly attempting to convince you of an opposing position. Oval flowers, large and small. Individuals being crammed into the same space.

A Mandala of peace extended from the center. It calms the distortion. The color purple. Calm. Black, although bold, absorbs the tension into the background.

All these thoughts I recognized, once finished, in my version of the Newton Fractal I produced from the original formula.

A Newton fractal is a boundary set in the complex plane which is characterized by Newton's method applied to a fixed polynomial or transcendental function. It's the Julia set of Newton's method. When no attractive cycles exist (of order great than 1), the iteration divided the complex plan into regions, each associated with the root of the polynomial. Extensive work by numerous scientists and mathematicians have unleashed the beauty of the Newton fractal.¹

The Newton fractal appears as intricate and beautiful as the Mandelbrot set. The complexities of fractal are on a higher mathematical level that I understand.

The Newton fractal was so named as a basis by other mathematicians for finding the root of a particular function. It was already known that a higher form of math was required.

The intricate patterns discovered inside the polynomial functions are some of most hauntingly surreal images you'll find.

I'd like to share some of filters I applied to the original fractal. The images produced display how the fractal can be transformed to add an array of colors and patterns.

NEWTONIAN FRACTAL ALIEN ART

For a special treat, I wanted to share my Newtonian fractal that was blended into a fractal alien invasion. Pairing my fractals with other art is intriguing.

Here are the iteration blending steps from the generative art program, "StarryAI".

I wanted to see how the fractal would look as an alien visiting earth. With StarryAI, I performed the following:

FRACTAL ART INPUT:

WORD PROMPT:
"Aliens visiting Earth."

RESULTING ITERATION PROGRESS
From left to right, below is the process in which the Starry AI program created my fractal art project from my Newton fractal.

FINAL OUTPUT:

It's an interesting concept working with generative art. The various programs I discovered handle the art process in different ways. Some of the programs are free to use. They do offer you the chance to upgrade. However, you can earn credits by performing certain tasks. I earn 5 credits daily.

I hope you like my Fractal Art Project.