Tony, You have good questions!

I'd like to know if anyone has found a "natural" or naturally occurring colour system with which to map the colours? I don't believe that there is any intrinsic or inherent coloring "built into" a particular fractal.

A (two dimensional) fractal is actually a field of numerical values. The coloring is used to replace the values with something more pleasurable to view. In the past I've tried to create some "natural" colors for fractals: Some time ago I created an approximation to the spectrum of colors visible to the human eye for coloring various images, including fractals. I had to work quite diligently to make my result reasonable. The association of particular numeric values of a fractal with particular colors Is called color mapping. I've also created a color map for coloring fractals that was an approximation of the heated object spectrum: Dim red, dark red, dark red-orange, dark orange, orange, orange-yellow, through shades of yellow and eventually white and finally blue-white. However, artistic-minded fractalists often create fractal colorings that emphasize partiacular features they locate in specific fractals. I believe this is one of the primary reasons that one finds non-intuitive or "non-natural" colorings of fractals.

the number of iterations is also arbitrarily chosen In fact, the number of iterations that take place at a particular location in a fractal is determined only by the values calculated by whatever formula is being iterated (calculated repeatedly) at that location.

When to stop calculating/iterating (to be able to assign a color to the result of the calculation) can be determined in a variety of ways. There are additional mathematical "controls" that one can apply to fractal generation/calculation -- other than coloring -- to change the appearance of a fractal.

the colouring which makes them so beautiful is more or less arbitrarily assigned to the escape values of the iterations of the Mandelbrot function The escape values being integer number of iterations makes the coloring of fractals also be discrete values -- each color is assigned to a specific number of iterations. This discreteness seems to also motivate a desire to carefully control the coloring of iterations...

Note that there are many, many other fractals in addition to the Mandelbrot fractal. And there are also non-integer/non-discrete methods of coloring fractals. I'm sure that others in the [Fractint] list can add to my observations about fractal coloring. - Hal Lane ######################## # hallane@earthlink.net ######################## -----Original Message----- From: Tony Kingsbury <tony.kingsbury@gmail.com> Sent: Saturday, August 13, 2022 5:53 AM To: Fractint and General Fractals Discussion <fractint@mailman.xmission.com> Subject: [Fractint] Re: Here's another new image from Albrecht which he calls "The New Mandelbrot" I'm new to the world of fractals. I understand that the colouring which makes them so beautiful is more or less arbitrarily assigned to the escape values of the iterations of the Mandelbrot function (I don't understand the math or the technical terms) and that the number of iterations is also arbitrarily chosen, and that the detail gets finer if the number of iterations is increased. I'd like to know if anyone has found a "natural" or naturally occurring colour system with which to map the colours? For instance, the wavelengths of the spectrum of the colours visible to the human eye. The Mandelbrot looks to me very much like the signature of a super-consciousness hiding in the mathematics, but if there is such a signature the colouring that makes it visible can't be random, or at the whim of whoever is running the program. I'd appreciate hearing about any research that might have been done into this. On Sat, 13 Aug 2022 at 21:28, Harold Lane <hallane@earthlink.net> wrote:

Albrecht's "The New Mandelbrot" was created using his multifractal_12 (MFR) formula.

Below are the "shortlinks" I created to his image and its PAR file on my server.

Here's Albrecht's suburb alternate Mandel: I especially like the "gold dust" sprinkled throughout his New Mandelbrot! https://bit.ly/50205-53-GIF

Here's its PAR file -- complete with the multifractal_12 formula: https://bit.ly/50205-53-PAR

- Hal Lane

######################## # hallane@earthlink.net ########################

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