These images are plots of the Mandelbrot set as generated by my program, gkII - Mandelbrot Mangler.

I had been reading an article on brainsturbator.com in which was asked:

Is it insane to propose that the most accurate name of God humans have found so far is "z = z^2 + c" the simple equation that creates the Mandelbrot set?

Which immediately brought to my memory the ludicrous idea that given a computer powerful enough and having enough time to zoom in far enough within the Mandelbrot Set, and that I just so happen to stumble upon the right coordinates, I might possibly find an image of me zooming into the Mandelbrot set, or a map of the village where I live, or infact anything that is possible in the real world, and the impossible too.

However, to this end, computers are horribly limited to the amount of precision with which they can represent floating point numbers. This allows mathematical calculations to be performed quickly inside a computer, but unfortunately it also limits how far into the Mandelbrot Set we can zoom.

Of course calculations requiring greater accuracy can be performed. For example I downloaded a 'arbitrary precision' maths library which was used to create an altered version of gkII which was supposed to allow me to zoom further into the M-Set. Unfortunately it was far too slow to be usable. Even when only extending the limit by a couple of decimal places.

The idea of finding images of the real world in Mandelbrot Set graphics, came about from the realisation that because of the infinite nature of the Mandelbrot Set, the act of exploring it, becomes more like the act of construction.

The Mandelbrot Set contains self-similarity at every depth. You can zoom in on a particular element and then continue zooming and you will find transformed versions of that element. Even the whole set, as shown on the right, is contained transformed within itself.

When you zoom into a particular element in the M-set, you can think of it as inscribing that element on a chain. A chain that is blank to begin with and like an infinite tree. Except imagine that the inscription made somehow transfers itself repeatedly, all the way to infinity.

It becomes possible to know your way around it. By selecting elements for the focus of the image, it is possible to design how the end point of the exploration will look.

Recall the idea that for a sculptor, the sculpture is already in the block of stone.

Consequently I often have ideas about how I want the end image to be. That is I figure out the elements I wish it to contain, the elements I want to zoom into. Make guesses about the number of times to zoom into this element and then swap to that element all without reaching the mathematical brick wall.

For the images in this gallery, I used the same start point for each. The start point is shown on the image above. These images are the ideas that worked within the confines of the fixed precision limit - or just things that caught my eye along the way.

Eye Candy

Comments