How to obtain M-sets of degree 11 or higher on Kalles Fraktaler

[greentexas]

It is possible to create Mandelbrot sets with power 11 or higher on Kalles Fraktaler.

• 1. Open Kalles Fraktaler.
• 2. Press File, and then Save, and then save your location as a KFR file.
• 3. Open the file in a program such as Notepad or TextEdit.
• 4. You should see a row that says "Power:" in the file. Change the power value to an integer greater than 10.
• 5. Save your file.
• 6. Open the KFR file on Kalles Fraktaler.
• 7. Explore!

These fractals take a while to render, but after around 1e20, if you are doing a zoom with few iterations, it should be quicker to render. I noticed this when trying to mimic this video a while ago: <a href="https://www.youtube.com/v/c_Xsd7jTQcg&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/c_Xsd7jTQcg&rel=1&fs=1&hd=1</a>

A similar procedure is why this video exists: <a href="https://www.youtube.com/v/qzuqh9b2Kpg&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/qzuqh9b2Kpg&rel=1&fs=1&hd=1</a>

where Kalles Fraktaler had to edit the KFR files to stretch the Buffalo over 9000 times.

NOTE: This procedure does not appear to work with non-Mandelbrot fractals.

[TheRedshiftRider]

I remember Karl (The developer) had at some point implemented up to power 20. Later the powers beyond ten were removed but only from the dialog so the actual formulas are still in there. For non-mandelbrot formulas/functions there has not been implemented higher than the power of five. Simply because they are different from the standard mandelbrot formula and because they are harder to implement.

Just out of curiosity, could you try something like 50?

[greentexas]

I have tried powers higher than twenty. I remember rendering a 1e100 image with a power 50 Mandelbrot months ago. These fractals take a while to render, but with patience, they can be done.

[TheRedshiftRider]

  Wow, I should really try that when I've got the time.

[Kalles Fraktaler]

Yes, I limited the power for standard Mandelbrot to 10 because Pauldelbrot's glitch correction method is not reliable on higher powers, even though the threshold is as high as 0.001 on powers higher powers. And having threshold higher than that makes most of the view indicated as glitch. But you are very welcome to explore higher powers
And Mandelbrot has Series Approximation for all formulas, thanks to knighty!

For non-mandelbrot formulas the formula needs to be analyzed in order to apply laser-blaster's abs function, so I am not able to do a generic arbitrary power formula as I did with the Mandelbrot powers.

As you see, all methods was invented by others, I am just the coder

[greentexas]

That is a very smart idea. This will prevent too many people from getting interested in the higher-power Mandelbrot sets by making them unobtainable without editing. Anyways, these fractals do take up much time to render.

Your program can't use "cookie-cutter" methods for fractals with large exponents. But I do have an idea on how you could use a "cookie-cutter" method. You could render the Burning Ship by rendering the M-set with powers 6 or more and then apply "abs" to it.

I have tried to render abnormal powers on a few fractals, but the program only gives me a colored version of the normal power. On the other hand, I have also tried to render negative powers for the M-set, but negative powers aren't very interesting in my opinion for zooming.

What I also think is interesting is how the formulas are organized. Many of the fractals have workarounds for higher powers. For example, the Perpendicular Burning Ship and its Mandelbar, which is a rotated version of the Perpendicular Burning Ship, look the same when the power is two.

If the power is three, the normal Perpendicular Burning Ship will become the Cubic Burning Ship Partial Imaginary. The Mandelbar Perpendicular Burning Ship, on the other hand, ends up being a rotated version of the Cubic Burning Ship Partial Real. When the power increases to four, the two fractals end up being rotated versions of themselves again.