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

M-Set 01

Mandelbrot Set Image 01

M-Set 02

Mandelbrot Set Image 02

M-Set 03

Mandelbrot Set Image 03

M-Set 04

Mandelbrot Set Image 04

M-Set 05

Mandelbrot Set Image 05

M-Set 06

Mandelbrot Set Image 06

M-Set 07

Mandelbrot Set Image 07

M-Set 08

Mandelbrot Set Image 08

M-Set 09

Mandelbrot Set Image 09

M-Set 10

Mandelbrot Set Image 10

M-Set 11

Mandelbrot Set Image 11

M-Set 12

Mandelbrot Set Image 12

M-Set 13

Mandelbrot Set Image 13

M-Set 14

Mandelbrot Set Image 14

M-Set 15

Mandelbrot Set Image 15

M-Set 16

Mandelbrot Set Image 16

M-Set 17

Mandelbrot Set Image 17

M-Set 18

Mandelbrot Set Image 18

M-Set 19

Mandelbrot Set Image 19

M-Set 20

Mandelbrot Set Image 20

M-Set 21

Mandelbrot Set Image 21

M-Set 22

Mandelbrot Set Image 22

M-Set 23

Mandelbrot Set Image 23

M-Set 24

Mandelbrot Set Image 24

M-Set 25

Mandelbrot Set Image 25

M-Set 26

Mandelbrot Set Image 26

M-Set 27

Mandelbrot Set Image 27

M-Set 28

Mandelbrot Set Image 28

M-Set 29

Mandelbrot Set Image 29

M-Set 30

Mandelbrot Set Image 30

M-Set 31

Mandelbrot Set Image 31

M-Set 32

Mandelbrot Set Image 32

M-Set 33

Mandelbrot Set Image 33

M-Set 34

Mandelbrot Set Image 34

M-Set 35

Mandelbrot Set Image 35

M-Set 36

Mandelbrot Set Image 36

M-Set 37

Mandelbrot Set Image 37

M-Set 38

Mandelbrot Set Image 38

M-Set 39

Mandelbrot Set Image 39

M-Set 40

Mandelbrot Set Image 40

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