Mandelbrot set deep zoom (HD)

Quick and dirty example of deep zoom on a fixed point near the Mandelbrot set.

Magnification rate is 2x every 2/3 of a second (8x every three seconds). Final magnification is about 2**240 or 1.8E72.

Real:-1.999992058192687313022543729145102991847847126539783513462412398802842769­683725402
Imag:-0.000000000001450204033707124987456880881808950903622191144103813894555017­097088328

I've since explored further and refined these coordinates for zooms of up to 2E275:
Real: -1.99999205819268731302254372914510299184784712653978351346241239880284393023150­84774892127559447760056252808041446563553194805889168776310285490614450736429953­75478866024333202372958521464046442639161141787629439733589289724815890177763835­096121061675026913413309691231725011972076
Imag: -0.00000000000145020403370712498745688088180895090362219114410381389455573582484­19930659467255909604840428519513516295408696481305264673019670684917184921565878­38673387113572614554545813415855172650467322561748969106686059449116724947320308­488642086833924759392799191924373703620251
where there's a babybrot requiring many more than 65536 iterations to show.

Category:

Film & Animation

Tags:

• mandelbrot
• fractal
• zoom
• psychedelia
• mandelbrot set
• deep zoom
• fingery
• poor quality encode
• hd
• silent
• Mandelbrot Set

[Kinokarte]

Very very nice. Do you know of a (relatively) simple algorithm to emulate "arbitraily" high precision math by just using single precision floating point operations? I would like to check this out as well.

[ToobMug]

Not exactly. It's normally done with integer arithmetic (using the same methods you learn in school for doing decimal arithmetic).  You can do integer arithmetic using floating-point operations but you'll have to limit your integer range to 24-bit to avoid errors.

If it's on a PC then you can just find an arbitrary-precision arithmetic library and use that.

[mf0rz]

What is the mathematical formula? Something like 1*1^½?

[ToobMug]

For each pixel on the screen, at coordinate (x, y), set c to (x + j * y) and set z to 0; then count the number of times you can repeat z = z^2 + c before the magnitude of z becomes greater than 2. Then you colour that pixel according to the number of iterations it took to get there. If that never happens then the coodrinate is part of the Mandelbrot Set (and will be coloured black in this video).

[mushroomagical]

Groovatronic!

[Jmsn72]

Sorry I can't give a more mathematical analysis as I suck at math but watching this was trippy as hell, especially while listening to some good psychedelic trance. Sorry if I sound like a hippie or stoner but it was an awesome video!

[FreshDumbl]

Someone should paint it in its entire detail :D

[Jupaerian]

maaaaaansolooooco

[Jupaerian]

de una

[InfinityOE]

@888madness Fractals use some of the easiest math... Just look up something like "Fractals for Dummies" on Google and I'm sure it will click eventually. I'm not good at math either.

[Kinokarte]

@ToobMug

The thing is, I wanted to do it on the GPU. With 1TFlop/s, one deep zoom image could be calculated in just ~ 1 second! I even found a website where someone emulated double precision with dual single precision. But unfortunately very high precision (like your 2^240) cannot really be done with Shader level 3 - but with level 4 or 4.1 it should be possible, and with 5/OpenCL/Cuda it definetly is.

On the other hand I have an almost-realtime Mandelbulb now... so I am happy for now ;-)

[BRUMARTUBE]

Take care of the numbers and the infinities will take care on themselves.