The Mandelbrot and Julia Sets

First is the basic Mandelbrot set, which looks like this:

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In this image, the whole fractal formula is visible. If you zoom in on a part of this image (or click on the image to see it at a larger size), you will see that the detail continues to reiterate itself, although in this particular fractal, the detail continues to change and mutate as you zoom further and further in.

Below is a 3x zoom, on the central left-hand side of the Mandelbrot set:

If you look carefully at this image, you can see the basic shape of the fractal continues to repeat itself. This detail continues to reiterate and mutate into infinity. Below are two more images, the first one is zoomed in 98x, and the second is zoomed in 698555x. Even in the second image, you can still clearly see the original shape of the Mandelbrot set, although it does look very different than the original un-zoomed image. No changes have been made to these images other than to zoom in and adjust the density of the gradient (colour palette) so you can see the detail clearly. The mandelbrot set contains infinite complexity. To see some more zooms of the mandelbrot set, have a look at Fraxplorer Gallery 8, Ultra Fractal Gallery 5 and Ultra Fractal Gallery 9.
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98x zoom

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698555x zoom

The Julia set

Here is the same progression, but this time with a Julia fractal. First is the basic Julia set:

A basic Julia
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Next is a Julia fractal with some slight modifications made to it. One way to get different results with the same formula is to give the computer non-standard values to use each time it calculates the formula (a reiteration).
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Then I took the same fractal and zoomed in on one of the central spirals; about 9x.

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