This past Friday, January 25, was the culmination of my winter study class "Math 14: Creating Fractal Art". Basically, for three weeks we were coding Matlab to produce some interesting fractal pictures. For the final project we had to make our own fractal and "upgrade" it using various artistic techniques of the Photoshop. I decided to take a rather different approach and use a somewaht simple fractal pictures but present them in the light of modern art ideas of Andy Warhol.
About the Art Mathematics and fine arts are similar or maybe even the same on many dimensions. Combining a beautiful mathematical concept of a fractal and style of a famous pop artist Andy Warhol my intention was to reveal a delicate relationship between the two.
In the universe of mathematics a local hero, the mathematician, tries to understand the world by formalizing the surrounding into the symbols and numbers of mathematics. Ultimately he explores the world in a purely formalized dimension. He uses this formalism for his advantage to reveal the hidden mysteries of the world and to leave irrelevant details aside.
In the universe of mathematics a local hero, the mathematician, tries to understand the world by formalizing the surrounding into the symbols and numbers of mathematics. Ultimately he explores the world in a purely formalized dimension. He uses this formalism for his advantage to reveal the hidden mysteries of the world and to leave irrelevant details aside.
An artist, alike the mathematician, does not leave the details aside. In the artist’s world, emotions, impressions and feelings are depicted as an inseparable whole. Irrelevant details are accepted and even welcomed in this world. Otherwise the art was boring.
But even though the two worlds where mathematicians and artist live might look very different, they are governed by the same universal laws. The essence does not change, only the form does. In the same way, fractal pictures cycle through the rainbow of colors, gain obscure looks and forms charming us with their thrilling looks yet leaving their mathematical nature intact.
About the Math
The following images are a close-up view of the Θ-Schottky Group circles generated using the Breadth–First Algorithm. The initial four circles were specified in matrix C, where column 1 is x-coordinates, column 2 is y-coordinates and column 3 is radii of each circle:
I then used Mobius transformations a, b and their inverses to generate the fractal image of my initial circles iterated nine times under the following conditions:
This is how the initial fractal looks like (before zooming into the corner and cycling through colours):
Or a 3-D version:
1 comment:
Keep up the good work.
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