FRACTALS: Geometry of Fractional Dimensions and Colors of Infinity
Experience the stunning beauty of computer-generated fractal images, where mathematical functions are used to create intricate patterns and shapes with an infinite level of detail. These images showcase the geometry of fractional dimensions and the colors of infinity, resulting in breathtaking works of art that are for me both mesmerizing and thought-provoking.
The World of Fractals: Objects with Fractional Dimensions
Have you ever wondered what makes leaves on a tree differ from one another, yet also all alike?
Or why small clouds repeat the design of larger ones?
Or why a stream in the mountains imitates the zigzag line of the peaks?
It's all part of a divine geometry, a magical world of mathematical spaces that can appear almost otherworldly to the unenlightened mind. This is the world of fractals: objects with fractional dimensions, where 1.4 dimensions create shapes that are infinitely complex and beautiful.
A Story of History
Let me share a story from my early days of computer art. It was my second year of exploring fractals, where it was easy to get fascinated. That summer, I took my daughter with me on a trip to the Netherlands, where we spent a month together.
I had the Performa, my first Mac, but it was slow and couldn't keep up with my fractal experiments. Undeterred, I had prepared fifty equations for the computer to render. I returned home, eagerly awaiting the results, curious to see how my equations had translated into images. Finally, after a few more days of waiting - 5 weeks altogether! - I was able to see the pictures.
They were breathtaking, a nod to the power of fractal geometry and the beauty of mathematical functions. My next, more powerful Mac rendered the images quickly, but alas! I couldn't find anything interesting anymore. Unfortunately, I hadn't written down my equations, Oh well, this experience taught me a lesson about the fleeting nature of art and the importance of seizing the moment.
