Fractal geometry is able to interpret irregular shapes like mountain ranges, coastlines and banks of clouds and describe them in mathematical terms. When this idea was first published in 1967 by Benoit Mandelbrot the term fractal had not yet been coined. The term fractal came from Mandelbrot in 1975 and has come to mean an object characterized by the repetition of similar patterns at ever diminishing scales. You will see why in a moment in this classic example. Imagine wanting to know the length of the coastline of Britain. Using Euclidean geometry a fairly straight outline of Britain would be used to find the perimeter of the island and it would be approximately 2400 km. Fractal geometry will measure the coastline using ever decreasing units of measure so that the resulting measurement will include all the nooks and crannies that make the true perimeter of the island and the coast is approximately 3400 km. No, Britain did not annex a neighbor’s coast to generate the extra 1,000 km. Instead, all the little fractions, or fractals, of the coast are included in the measurement. These nooks and crannies are referred to as self-similar in fractal terms. This means the coastline repeats a pattern of nooks and crannies at ever diminishing scales. In the case of the coast, the small little bays are very similar to the next larger bay and that bay is shaped a lot like the bigger bay it is a part of and so on.
Once a month I will send out a fascinating email that will give you new and interesting information about fractals.
The majority of these posts will draw from my thesis, “The Art of Fractals for the Mathematically Challenged”. I am fascinated with fractals but by no means can compute the math.
Blog 1…. here we go!!
One of the most difficult things about being an artist is coming up with new and interesting ideas that are engaging to work on that are artistic and emotional things of beauty. This means that searching for inspiration in an ongoing endeavor for most artists. It was during one such search that I stumbled upon a fractal. There it was on my computer screen, a thing of beauty. I had never seen one and had no idea of how it was created. I wanted, I needed, to know more. Thus began an ongoing exploration into what many consider to be one of the most significant discoveries of our time, the fractal and fractal geometry. The purpose of this blog is to explain what a fractal is, what they can do, why we like them, where they are found and their effects on the world of art.