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Author Topic: Basic Mandelbrot question: out-coloring modes  (Read 1162 times)
Description: Just how fractal is out-coloring?
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Posts: 39

« on: October 25, 2014, 10:46:00 AM »

I have a question about the Mandelbrot and Julia sets and what Xaos calls "out-coloring modes".

 Basically, how "fractal" are out-coloring variations, as provideded in Xaos,  or are they simply fractal-like or fractal-influenced? For example, using Frax on my iPad, I produced these images, attached. Now they are all representations of the simplest Julia set, a perfect circle in the middle of the large mass of the Mandelbrot set. They are 4 dramatically different images of the same fractal. Are they fractal images only technically? Is the coloring, and the out-coloring shapes and textures just decoration at the whim of the programmers who designed the app? Or is this decoration a fractal in its own right?

* image.jpg (12.38 KB, 191x143 - viewed 387 times.)
Fractal Senior
Posts: 7044

formerly known as 'Trifox'

« Reply #1 on: October 25, 2014, 12:35:13 PM »

out-coloring-modes definition:
the out coloring describes how a point that DOES NOT belong to the fractal is colored, belonging to the fractal are all points that do not escape, for the julia set above it is ALL points that are below the unit-circle, becuase each iteration a number below 1 is multiplied by itself making it smaller and smaller, so, hence the black area because those points iterate forever because they "shrink"

and the out coloring is then all points that do escape at a certain point, check my mandelbrot iteration video for clarification, this is applied to any escape time fractals, hence the name color-by-escape time and in the most basic form the color is just the escape iteration as demonstrated in the video below

so, the out coloring then can apply various methods to achieve a certain result, frax is using a fairly distinguished way to determine outside colors, for once it uses orbit trapping of complex shapes which means in the iteration loop a distance to a shape (e.g. a circle) is determined which influences the outside coloring

the pictures you posted apply various other methods, for example the circle image you got there just applies a color gradient to the distance to zero, but the coordinates can as well be applied to a noise texture as in the lower left

i would vot for "yes" that says the outside regions can be considered fractal as well, especially when the outside regions are put into another fractal method again wink you see there is much to play with and much to layer frax does an excellent job in this!

video visualisation what the computer does
<a href="https://www.youtube.com/v/ce0lms78nt4&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/ce0lms78nt4&rel=1&fs=1&hd=1</a>


divide and conquer - iterate and rule - chaos is No random!
Strange Attractor
Posts: 253


« Reply #2 on: October 30, 2014, 07:44:31 PM »

how it works???

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