Googol

[Pauldelbrot]

Googol



http://www.fractalforums.com/index.php?action=gallery;sa=view;id=12000

Magnified exactly one googol times from a view of the whole set. Apologies for the shoddy AA; this was also used as a slide in the Brief History contest entry, and time constraints prevented rendering it with more than about 3x3. As it is it took four days to render.

This image is in fact a zoom into the Butterfly image, which was also used as a slide in the same section of the same video. Close inspection of the orange band just inside the prominent, large red band will show tiny butterflies on twigs. The red band actually has clusters of three butterflies inside the bulges, but they're unrecognizably tiny in the image.

[KRAFTWERK]

Cool Paul, I like Googol!
You head of to render a Googolplex zoom next I hope... 

[Pauldelbrot]

Thanks. Googolplex will have to wait until 2046 or so. Sorry.

[KRAFTWERK]

OK, I'll check in from the retirement home then! 

[asimes]

A googol is crazy, wow. I just wanted to make sure I understood, if the boundaries of a normal Mandelbrot set go from -2 to 2, then that goes from -2/10^100 to 2/10^100?

[Pauldelbrot]

A googol is crazy, wow. I just wanted to make sure I understood, if the boundaries of a normal Mandelbrot set go from -2 to 2, then that goes from -2/10^100 to 2/10^100?

It's a region fitting within a square of the same size, yes, but the exact coordinates you gave would be a blank black square. Instead, the width is the same, the height somewhat less, and the center coordinates are, obviously, elsewhere (in fact rather close to -1.75 rather than 0).

[asimes]

I didn't mean coordinates, I meant the boundaries (what value represents the left and right side of the screen on the real or imaginary axis). For example, if a normal Mandelbrot screen goes from -2 to 2 on the real axis, it has a width of 4.

[asimes]

I just reread what you wrote, sorry, I forgot that it wouldn't be exactly centered, that makes sense now.