# Thread: The Buddhabrot set: the Mandelbrot set's spiritual cousin

1. ## The Buddhabrot set: the Mandelbrot set's spiritual cousin

Many of you may have heard of the Mandelbrot Set. It's regarded by many as the most beautiful visual construction in mathematics. Generated by a simple formula, this is what it looks like. And if you zoom in on it, it repeats itself literally forever at the boundaries, which is what fractals are all about.

But you may not have heard about the Buddabrot. This is also derived from a simple formula, closely related to the Mandelbrot construction. It astonished its discoverer, Melinda Green. It looks like this.

This is not a joke: the math really does generate this image. There are various different depictions of it, depending on the specifics of the variables that are graphed out. Here's another version:

And look at this depiction of the 'heart chakra" in the model.

The images on this page were all generated using a technique I developed in 1993 to render the Mandelbrot set. It's important to realize that it is not a different fractal from the Mandelbrot set, but simply a different way of displaying it. Clicking on some of the images will take you to a normal rendering of the exact same area, but using the traditional Mandelbrot technique.

Note that even though the images resemble Hindu art, they were actually generated completely automatically, without any sort of human artistic intervention. When I first tried using the new technique, I had no idea what the images might look like and was completely surprised by the results.

I was later pleased to learn that a computer artist named Lori Gardi, who I had described this technique to several years ago, has since devoted a great deal of her creative effort to generating various high-resolution images using the technique.

She named it Buddhabrot, which is a name I instantly loved and have adopted. Lori's web site contains some reduced examples of her work along with her writings into the mystical connections she's made between the Mandelbrot set and Buddhism.

The above image [the first one above] shows the overall entire Buddhabrot object. To produce the image only requires some very simple modifications to the traditional Mandelbrot rendering technique: Instead of selecting initial points on the real-complex plane one for each pixel, initial points are selected randomly from the image region or larger as needed.

Then, each initial point is iterated using the standard Mandelbrot function in order to first test whether it escapes from the region near the origin or not. Only those that do escape are then re-iterated in a second, pass. (The ones that don't escape - i.e.. which are believed to be within the Mandelbrot Set - are ignored).

During re-iteration, I increment a counter for each pixel that it lands on before eventually exiting. Every so often, the current array of "hit counts" is output as a grayscale image. Eventually, successive images barely differ from each other, ultimately converging on the one above.

I'm the most unreligious person you could ever meet, but it's hard not to think of this image as revealing God hiding in the Mandelbrot Set. And not hiding in some tiny corner, but a single image hiding in plain sight at full-size, suggesting that the Hindus were the ones who got it right.

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3. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

Wow, spectacular!

Bill, as a budding polymath, do you know if we have any idea what the underlying mathematics (as if I could understand any of it lol) may look like? The 1's and 0's so to speak? I didn't see any reference to that on her blog.

Or is this the wrong way to look at it/think about it?

I always like to look under the hood of things.

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5. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

• Posted by Gracy May (here)
Wow, spectacular!
Posted by Gracy May (here)
Bill, as a budding polymath, do you know if we have any idea what the underlying mathematics (as if I could understand any of it lol) may look like? The 1's and 0's so to speak? I didn't see any reference to that on her blog.

Or is this the wrong way to look at it/think about it?

I always like to look under the hood of things.
—> https://simple.wikipedia.org/wiki/Mandelbrot_set

(Better than I could explain it! )

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7. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

I found this on the Wayback Machine. (Tragically, the website fractalbuddha.com is no more)
Fractal Buddha - Vision of the Jeweline Buddhaverse

Here are some pictures from Vision of the Jeweline Buddhaverse art show:

From your center in Eternal Being,

Energy intent swirls outward to become beings,

Angels,

Pattern beings,
Generations of light

The Third Millennium

~~~

Buddha has many forms
of transformation
and incarnation,
and can manifest himself
in manifold ways
according to the ability of each person.

The Teaching of Buddha

~~~

"Asato ma sat gamaya

Tamaso ma jyotirgamaya
Mrtyorna amrtam gamaya"

"From the unreal,
From darkness,
From death,

~~~

What is Fractal Buddha?

Fractal Buddha (The Buddhabrot Set) is created using the famous Mandelbrot Set equation, zn+1 = zn2 + c where z and c are complex numbers. Each number in the complex plane (between 2 and -2) are put through this equation many many times over (iterated). A point is plotted on the screen for each iteration of each pixel in this area of the complex plane. Note: only the points outside of the Mandelbrot Set are used to generate Fractal Buddha.

The algorithm for generating Fractal Buddha is as follows: For each point in the complex plane (outside the MSet), iterate through the equation, calculating a new (complex) point for each time through the loop. Plot the point by incrementing the pixel value at the position of the new complex point. The more times a point is 'hit' by this equation, the brighter the pixel will appear. For best results, use only points close to the edge of the Mandelbrot Set.

Special thanks to Melinda Green for showing me this technique for generating the beautiful Buddhabrot images. Link HERE;

Here is Melinda Green's description of the Buddhabrot algorithm:

Galaxies swirling
Forever bound
By forces invisible
Divisible
Complex interleaving
Leaving behind an image
Of its former self

FractalWoman

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9. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

That’s quite perfect that’s about how we look in perfect Universe.

If it’s something it reminds me of in this world
it would be something like plasma emanation above candle flame,
bubbles and rainbows.

Sublimely symmetrical time-Space manifold.

Transforming all imperfections back to their original state

Purnat
Purnam Udachyate
Purnameva vashishyati

Om Shanti: Shanti: Shanti::

Thank you Bill

🙏❤️🙏🕊🕊🕊

Perhaps it’s more like how the Universe gives birth to a star

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11. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

Although the creation of many crop circles is debatable and no one really seems to come forward to claim their creation (further adding weight to the theories that they are not man-made), we do know that the complex crop circle located in a Cambridgeshire field, which appeared in 1991, was created by man. According to the BBC, two men named John Lundberg and Rob Irving were asked to recreate the Mandelbrot Set, to test the theory it was possible it could have been made by humans, and after recreating the design in just four hours, Lundberg is believed to have admitted to also creating the original but showed NO EVIDENCE how!

The Hardest Mandelbrot Zoom Ever In 2014,10^198 : New record - 350 000 000 iterations

I remember, as if it was yesterday, the moment I saw "The Mandelbrot Crop-Circle" being discussed Live on "The Larry King Show" CNN 1991 where infamous elderly hoaxers Doug Bower & Dave Chorley confirmed they did NOT make that one when they were confronted on live TV!

As I knew how important people see that a ±40 meter (±132 feet) by ±60 meter (±197 feet) Perfect Fractal was made! ... To my knowledge there was and still is no computer-printer printing that perfect shape of 40 meters wide! ... Notice that also inside the Mandelbrot Crop-Circle all plants were harmonious aligned as if it behaves like iron fillings on a peace op paper with a magnet beneath it!

cheers,
John Kuhles
February 6th, 2020

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13. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

wow !! ..... looking into the 4 pics posted they seem to my eyes to have an usual motion , remarkable .
Bill , great thread bringing this Buddhabrot to our attention here .
I'll go check Melinda Green's blog now .
cheers

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15. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

Nice thread Bill. I was fascinated with the Mandelbrot Set, sacred geometry, and fibonacci in the early stages of my awakening. I have seen this shape prior but never equated it to Buddha, which you can see has a close resemblance.
I had created my very first music video on YT about 10 years ago using fractal images/sacred geometry etc, with music by guitarist Joe Satriani. Have a peak.

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17. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

Found another amazing masterpiece:

Reminds me of some phenomena, all inclusive anyway When I was a kid I used to do this little exercise before sleep because I found it too interesting. Pressing my eye bulbs gently with lids closed, I’d see these amazing patterns like mandalas or intriguing nets, of all colours, deep and unique colours too.
No need to go deeper to this now.

But another thing fractal geometry and the Buddhabrot and Mandelbrot remind me of is patterns on Kashmiri shawls, carpets and other weaving.
Remember watching them from my childhood too and thinking they’re infinite and continuity of one. The same motive often repeats itself endlessly coming as if one of another.

Now I’ve found there’s a name for those patterns, not only that, their very explanation points out that old Persians understood something about Mandelbrot

Buta

Boteh Jehgeh...”ancient motif” of Indo-Iranian culture..representative of sacred tree of life, sun, Phoenix, etc.

Buteh

Observe the similarity ..marvel.

My old shawl,

🌈😷🙏

The Armenian Origin of Buteh symbol

Boteh meant among else “eternal flame” in Zoroastrian temples. Thistle as in “flower of life” in Parsi, mentioned is also similarity to the constellation Bootes.

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19. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

Number 3 is definitely my favourite.

The “Old Universe” of harmony and beauty

Are we coming or going

Are we coming n going

What remains to be done

What’s not to be done

Sarvam Brahma Mayam

This all is also That

💫

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21. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

I agree Agape, the 3rd video has a very peaceful and calm vibe.

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23. ## Re: The Buddhabrot set: the Mandelbrot set's spiritual cousin

Found somebody has done their piece of homework on this amazing topic:

from Dr Anja Karina Pahl of the UK,
interdisciplinary scientists, catalyst and innovator
website says “coming soon” but there are many good references
to her on the internet.

Somehow I was able to obtain abbreviated pdf version of her book
that has only 36 pages but it’s worth viewing.

Book preview: The Mask of the Buddhas

May we understand everything little better
The lock and the key
The right and the left
Love and reason

Happy Valentines

🙏🌸🌸🌸🙏🕊🕊🕊

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