joslinrashleigh
ertertre
13/02/14
The following 8 images and 2 videos depict fractals generated in a program called 'Xaos Fractal'. It is less the visuals (although fractals are defined by a very unique aesthetic) and more the theory that is relevant to my post-digital concept.
A fractal is a visual representation of an infinite iteration of an algebraic function using imaginary numbers (z) , mapped on an complex plane which allows each number a geometric representation as a coordinate.
The iterations are recursive, meaning you put the output of the function straight back into the same function, essentially squaring the output. This is repeated infinitely.
Depending on whether the output stays bounded (within the imaginary plane) or escapes to infinity - a pixel is coloured either black (for bounded outputs) or a colour dependant on the speed with which the iteration escapes to infinity.
The famous Mandelbrot set is the set of values of 'c' (an imaginary number) in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial. An easy to understand but theoretically complex equation:
z=z^2+c
imaginary numbers are combinations of the real and imaginary so z = a+bi
A fractal by definition is a mathematical set that typically display self-similar patterns. It is the architecture of nature... coastlines, veins, lungs, ferns, trees, shells, flowers. The fibonacci sequence is itself a fractal. The internet and the structure of the rate of technological development both have obvious fractal dynamics. The fractal can theoretically be zoomed-in on infinitely as there are an infinite amount of numbers, ipso facto functions and iterations.
ertertre
13/02/14
The following 8 images and 2 videos depict fractals generated in a program called 'Xaos Fractal'. It is less the visuals (although fractals are defined by a very unique aesthetic) and more the theory that is relevant to my post-digital concept.
A fractal is a visual representation of an infinite iteration of an algebraic function using imaginary numbers (z) , mapped on an complex plane which allows each number a geometric representation as a coordinate.
The iterations are recursive, meaning you put the output of the function straight back into the same function, essentially squaring the output. This is repeated infinitely.
Depending on whether the output stays bounded (within the imaginary plane) or escapes to infinity - a pixel is coloured either black (for bounded outputs) or a colour dependant on the speed with which the iteration escapes to infinity.
The famous Mandelbrot set is the set of values of 'c' (an imaginary number) in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial. An easy to understand but theoretically complex equation:
z=z^2+c
imaginary numbers are combinations of the real and imaginary so z = a+bi
A fractal by definition is a mathematical set that typically display self-similar patterns. It is the architecture of nature... coastlines, veins, lungs, ferns, trees, shells, flowers. The fibonacci sequence is itself a fractal. The internet and the structure of the rate of technological development both have obvious fractal dynamics. The fractal can theoretically be zoomed-in on infinitely as there are an infinite amount of numbers, ipso facto functions and iterations.