Mandelbrot Circles?

[murkey]

I was watching some awesome zooms and came across this one:

<a href="https://www.youtube.com/v/PD2XgQOyCCk&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/PD2XgQOyCCk&rel=1&fs=1&hd=1</a>

Amazing. The description says:

This took ~4 weeks to calculate the log(z) plane (or 'side scrolling' plane) and about 1 hour to assemble the video.
1920 points were calculuated per circle
164353 circles were calculated
the coloring is my standard histogram equalization in the side scrolling plane before mapping back to z plane (thanks to phaumann for this idea)

So my question is... what circles? And what's the log(z) plane?? I'm pretty new to this stuff so I apologize if I missed something obvious or didn't search enough. Thanks!

As a token of my gratitude, here's a render I just did with libgmp. Hope it's not too hard on the eyes:
https://dl.dropboxusercontent.com/u/24793835/daily2.png

Thanks again

[cKleinhuis]

as far as i know it is called mercator maps, which can encode a full zoom sequence in a single image, i have not done it myself, but here are some links,
perhaps someone else can point you to a concrete mandelbrot example

http://en.wikipedia.org/wiki/Mercator_projection

https://www.flickr.com/photos/arenamontanus/sets/72157615740829949/

[claude]

Here's an animated SVG I made some years ago that tries to explain how to convert 2x zoom levels into an exponential strip (this technique has lots of names)

http://mathr.co.uk/mandelbrot/exponential_strip.svg

The red pixel on the right is made up of a linear interpolation of 8 pixels on the left.

But you wouldn't want to calculate the exponential strip image in this way unless you had no other option - it's much less efficient than rendering an exponential strip directly and then generating 'flat' frames from it.

As ever, Mu-ency has a useful page:

http://mrob.com/pub/muency/exponentialmap.html

[murkey]

Awesome, thanks!! I won't claim to fully understand yet but this is a good start