Week 8: Fractals and Chaos Theory

Fractal generated from the Mandelbrot Set.

In this week’s reading, Wilson commentates on the topic of fractals. Fractal geometry, with its almost unpredictable and spontaneous nature, especially to its viewer, attributes its characteristics from the Chaos theory.

As we learned earlier in the quarter from previous readings, the Chaos theory embodies systems that exhibit nonlinear characteristics, which makes them extremely hard to predict and spontaneous. Such a system captures the infinite complexity of such processes, a phenomena that can be shown through fractals.

I think these characteristics are some of the main reasons why I have always had great appreciation for fractals and have been always able to watch videos of fractals for hours on end. The unpredictability of their designs and directions make them completely unique and diverse in their designs. Every fractal that I have seem are always different and always seem to veer in different creative directions.

Still, the first time that I remembered learning about fractals was probably in my Algebra 2 class freshman year in high school. I think what really drew me to fractals was the fact that such systems involved both mathematical and artistic qualities. I’ve have always been interested to fusions of processes almost directly opposite to each other, and fractals exhibited this almost quite exactly.

What’s interesting about fractals to me as well is the fact that the aesthetic portion of this system is all based on its mathematical unpredictability. So in other words, the images generated from these mathematical operations, that the viewers see and can also see as beautiful, are all images that computers and mathematical systems generate at random based on a certain mathematical algorithm. The combination of colors and shapes are all products of equations and codes that can in turn create a spontaneous visual piece of art.

In the Mandelbrot set, probably one of the most widely-known fractals, the function for this fractal is based on the following polynomial:



Using this equation, and a complex coordinate plane, it can be iterated repeatedly in order to create a fractal image. Although this is an extremely brief explanation for this particular fractal, it still displays the use of mathematics to create a form of art.

With the addition of computer resources, one can use such mathematical functions to create fractals in terms of setting up iterations and infinite loops to create never-ending images.

Beauty in things that someone would most likely not think to find it is what draws me the most to this topic and the generative and random nature of fractal art is simply quite amazing.

–Dahlia Dominguez


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