Hello,

I have been working with a formula for a while, which I have been calling Mandalamandelbrot and Mandaljulia, because it creates nice patters with circular symmetries depending on the location and parameters used. Here are a few examples:
https://www.deviantart.com/rychveldir/art/Almond-Ship-931583199
https://www.deviantart.com/rychveldir/art/Mandala-Chain-912805646
https://www.deviantart.com/rychveldir/art/Green-Stars-904525576
https://www.deviantart.com/rychveldir/art/Lovely-889644244
And the little circles used for this are also shots from the same formula:
https://www.deviantart.com/rychveldir/art/Tribute-to-Benoit-B-Mandelbrot-905071991

A few days ago I simplified it a lot, so that instead of changing the formula between iterations, it just repeats the same iteration, then I use inside coloring. Here are a few examples of what it can do with the Julia version:
642d27e9d65e7.jpg
642d27e9d9405.jpg
642d27e9da57c.jpg
642d29641dce4.jpg

And here's a "Mandelbrot" version
642d27e8b135d.jpg
All these imgaes have a fairly low iteration count (in the high single or low double digits!), and none of them are deep zooms, so unlike my Coupling Loops, it's super fast as well. smile

The iteration is fairly similar to the Burning Ship, except that I am using one exponent inside the abs function and then another outside of it:
642d28890e385.png
where a and b can be integers, float or even complex numbers. Generally the MB version looks distorted in many places, but the Julia Sets do not!

The current working title is burning_what2, but I need a better one before making it public!

Hello, I have been working with a formula for a while, which I have been calling Mandalamandelbrot and Mandaljulia, because it creates nice patters with circular symmetries depending on the location and parameters used. Here are a few examples: https://www.deviantart.com/rychveldir/art/Almond-Ship-931583199 https://www.deviantart.com/rychveldir/art/Mandala-Chain-912805646 https://www.deviantart.com/rychveldir/art/Green-Stars-904525576 https://www.deviantart.com/rychveldir/art/Lovely-889644244 And the little circles used for this are also shots from the same formula: https://www.deviantart.com/rychveldir/art/Tribute-to-Benoit-B-Mandelbrot-905071991 A few days ago I simplified it a lot, so that instead of changing the formula between iterations, it just repeats the same iteration, then I use inside coloring. Here are a few examples of what it can do with the Julia version: ![642d27e9d65e7.jpg](serve/attachment&path=642d27e9d65e7.jpg) ![642d27e9d9405.jpg](serve/attachment&path=642d27e9d9405.jpg) ![642d27e9da57c.jpg](serve/attachment&path=642d27e9da57c.jpg) ![642d29641dce4.jpg](serve/attachment&path=642d29641dce4.jpg) And here's a "Mandelbrot" version ![642d27e8b135d.jpg](serve/attachment&path=642d27e8b135d.jpg) All these imgaes have a fairly low iteration count (in the high single or low double digits!), and none of them are deep zooms, so unlike my Coupling Loops, it's super fast as well. :) The iteration is fairly similar to the Burning Ship, except that I am using one exponent inside the abs function and then another outside of it: ![642d28890e385.png](serve/attachment&path=642d28890e385.png) where a and b can be integers, float or even complex numbers. Generally the MB version looks distorted in many places, but the Julia Sets do not! The current working title is burning_what2, but I need a better one before making it public!
 
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Burning Mandala.

Or just Burning Man if that’s your scene. Or Giordano Bruno because, well, you know.

Great pics, especially the last one. I’m looking forward to messing around with this.

Burning Mandala. Or just Burning Man if that’s your scene. Or Giordano Bruno because, well, you know. Great pics, especially the last one. I’m looking forward to messing around with this.

http://www.youtube.com/fractalzooms

 
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I published the formula a few days ago and went with your name suggestion Eric smile Note that the formula acutally does
z = abs(z^Exp1)^(1/Exp2) + #pixel
This is, in my opinion, a bit more intuitive, because if Exp1 and Exp2 are close, the exponent of the final function is close to 1, which results in certain behaviors seen by such a function. IMHO the most interesting results can be seen when Exp2 is about Exp1 - 1, or close, but in general they can also be nevative or even complex. Making Exp2 complex doesn't cause discontinuities the way it would for a normal Mandelbrot set, so it's quite interesting to play with that.
Exp1 generally decides the symmetry, you get n-sided symmetric shapes in the image where n = 2*Exp1. Can't wait to see what others come up with, here's two images I published already. The first one uses Exp1=3.5, which results in 7-sided symmetry.
6448d46137e06.jpg
The second one uses Exp1 = Exp2 = 1.5, which actually creates 3-sided symmetries:
6448d4613de43.png
Both are Julia Sets, the MB-Variants are quite messy in most cases and, because the formula is non-conformal (i.e. angle-preserving) you end up with a lot of distortion.
But you can also just zoom into the MB-Variant and un-skew the image for similar results. smile

The base of the formula is the Buffalo fractal, which is a sibling of the Burning Ship:

Burning ship: abs(z)^n
Buffalo: abs(z^n)
Burning Mandala: abs(z^Exp1)^(1/Exp2)

Have fun!

I published the formula a few days ago and went with your name suggestion Eric :) Note that the formula acutally does z = abs(z^Exp1)^(1/Exp2) + #pixel This is, in my opinion, a bit more intuitive, because if Exp1 and Exp2 are close, the exponent of the final function is close to 1, which results in certain behaviors seen by such a function. IMHO the most interesting results can be seen when Exp2 is about Exp1 - 1, or close, but in general they can also be nevative or even complex. Making Exp2 complex doesn't cause discontinuities the way it would for a normal Mandelbrot set, so it's quite interesting to play with that. Exp1 generally decides the symmetry, you get n-sided symmetric shapes in the image where n = 2*Exp1. Can't wait to see what others come up with, here's two images I published already. The first one uses Exp1=3.5, which results in 7-sided symmetry. ![6448d46137e06.jpg](serve/attachment&path=6448d46137e06.jpg) The second one uses Exp1 = Exp2 = 1.5, which actually creates 3-sided symmetries: ![6448d4613de43.png](serve/attachment&path=6448d4613de43.png) Both are Julia Sets, the MB-Variants are quite messy in most cases and, because the formula is non-conformal (i.e. angle-preserving) you end up with a lot of distortion. But you can also just zoom into the MB-Variant and un-skew the image for similar results. :) The base of the formula is the Buffalo fractal, which is a sibling of the Burning Ship: Burning ship: abs(z)^n Buffalo: abs(z^n) Burning Mandala: abs(z^Exp1)^(1/Exp2) Have fun!
 
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