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In this movie I am experimenting with 2 things
- Two long wave colors are applied, one black and one white, to emphasize the final minibrot. It is kind of cheating since these waves are fine tuned to the iteration values surrounding the minibrots. But I think it looks good and the intention was to mimic Pauldelbrot's excellent zoom series.
- The end is not how they use to end. Maybe you have seen it many times before, but I have not

http://www.youtube.com/watch?v=rj52_WwUvEE

I want again thank mrflay and Pauldelbrot for the discoveries of the methods to render Mandelbrot fractals previously unbelievably fast - and correct. Without your generously shared discoveries this movie would never have been created. And even though Kalles Fractaler is 100 times faster than the traditional programs, it is reachable to make Mandelbrot renders even many times faster. That may be something for the future...

Nice! The coloring is excellent, and I liked the surprise ending. For some reason I was half-expecting it to scroll upon another minibrot, even though I knew it was impossible. You'd have to cheat to make that happen!

I wonder how long the distance is to the nearest minibrot on the same depth. Or even any other minibrot. Is it even possible to calculate? Considering this is magnified a googol times a hundred million, the distance may be the same range. Fascinating thought...

How to do this???? Maybe, you reuse reference but generate approximation for every moment.....................................................................................

It reminds me Side-Scrolling plane, but this is not SS-plane ;-)

That's actually a nice question to think about. How exact do you want the same depth to be? Is there a finite amount of minibrots on a given depth? I would think so, because the complex area in which the mandelbrot is drawn is just a finite space. While the length of the border of the set is infinite, the area of the set is finite. Perhaps every mini has its own exact level of depth? If this is true, I would like to see the sequence of those shapes.

The easy answer would be infinitesimal close, since there are lots of minibrots on any border of any (mini)brot.

Yep, the word 'visible' fell off :).

I know there are a well defined numbers of minibrots for each number of terms included in the expanded Mandelbrot formula, the details can be found in other threads. But I don't know if there is a general relationship to the depth that can be taken as far as to googols. But if it is possible to know how many the minibrots are, it would at least be possible to find the average distance since we know the magnification.

That's something nice to think about.

If we keep expanding the Mandelbrot formula, there would be infinite number of minibrots. In that case the average distance would approach zero. But I guess you're talking about some relative distance, relative to the size of the reference-minibrot. In that case I think the space between two size-similar minibrots gets filled up with more and more sizes, which would mean that the average relative distance approaches infinity. It's nice how discrete or limited math joins the infinite stuff in the Mandelbrot set.

What I am aiming for is a relationship of the same sized minibrots, like
- the unzoomed Mandelbrot has one root and one 'Brot' in zero.
- the second level has 4 Brots, i.e 4 roots to the 4th degree equation. Maybe magnified 4 times make them sufficient visible.
- the 100th level has 200 Brots, i.e. 200 roots to the 200th degree equation. I think? Is a magnification to 100 enough to make them sufficient visible?
- the googol-th level has 2 googols Brots? But is a magnification to a googol the same as the googol-th level, because the iterations is only some 100,000. Or is it more reasonable to say it's the 100,000th level?

The only thing we know for sure is the size of the whole view, in the unit of the minibrot, it's a googol. So how far must we scroll in any direction to find another minibrot of the same size or bigger?