Fractal was defined by Benoit Mandelbrot, from the latin “fractus”, meaning irregular or fragmented. Essencially a fractal is a visual expression of a repeated pattern or formula that starts simply but gets more complex over time. I chose to research into them more closely for the liminal project due to their ability to connect the technological and the human, the maths and the arts and most significantly they can be seen anywhere. I realised the potential for fractals within this project due to the patterns of the rain in the drawing weeks sketches of the glass ceiling, nature is known to have produced fractals first. The fractals in nature are well known and well used; the fractals in leaves, for example are used to determine how much carbon is contained with its corresponding tree.
“A fractal is a pattern made up of shapes that can go on exactly the same for infinity, however they are usually contained within a finite amount of space.”
This was the logic of Lewis Fry Richardson, in the early 20th century; as he reasoned that the length of a coastline will depend on the length of the measurement tool. However the fact that a fractal can be used to infinity was put forward by Helge Von Koch, the creator of the Koch Snowflake. The snowflake is created by taking a triangle then layering another over the top, before continuing to do so on each of the corners of the triangles and then again on each of the corners of those triangles, reaching towards infinity on each corner, as each will create two more corners and each of those two more and so on.
The four others I looked into were; the Sierpinski carpet; first described by Waclaw Sierpinski in 1916, it uses the topological space of a square, then creates a centre square to act as the core as it then divides the original square into having a square at every direction from the centre. Then each of those squares has another set of squares at every direction from it, and again, ad inifitum. There was also the Peano curve, first created by Ginseppe Peano in 1890, which consists of interlocking lines that constrict an alternate pattern according to each collumn. The T-Square was explained as a two dimensional fractal, it follows the rule that you subtract a square a quarter the area of the square plane you would be working on, from the centre and repeat. Finally there was the Harter-Heighway Dragon curve; which uses two connecting lines at a 90 degree angle and turns them another 90 degrees and adds the previous diagram onto the end, and repeats. The formula used is; -X –>X+YF+, Y–>FX-Y.
Fractals are well known and are throughly researched, including techniques for generating them, mathematic equations for accurate reproduction, all along with the various fractals that are famous for their advance in maths, or their point proven in logical thinking. Some can create fantastic images; the randomly generated Brownian tree, the perlocation, strange attraction, the escape time or the generalized lyapunoc logistic fractals (occasionally with an iteration sequence). However these are computer generated; so I wanted to create fractals in a way that a computer couldn’t.