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Approaching the unapproachable largest cardioid these beautiful small digits are found. The boundary becomes thicker, convoluted and unpredictable. Too, the density of the minbrots (islands) increases. Nearing the cardioid the amount of compute, time required, to reveal these lovely clouds very rapidly becomes impractical. These are not extreme magnification images, though close to the primary cardioid.

Majestic:
(http://www.fractalfreak.com/Images/Majestic_thumb.png) (http://www.fractalfreak.com/HQGallery1/Majestic.html)

Purple Down Draft:
(http://www.fractalfreak.com/Images/PurpleDownDraft_thumb.png) (http://www.fractalfreak.com/HQGallery1/PurpleDownDraft.html)

The first one is a beautiful snapshot which reminds of a satelite picture of a mountain

They're both beautiful. But the second one isn't on the main cardioid; it's at the edge of the big period-2 disc right next to it. :)

Yes you're correct. The first image is off the primary cardioid, not the second.

The first one is beautiful, like cracked, dried blue mud....

Both are awesome!

I also found it curious that those (older?) deep zoom movies mostly zoom in on some outer parts, probably to keep the computation time down. Closer to the circle-like edge of the Mandelbrot the boundary of the sets seems to curl more and more on itself, which gives denser images. It it true that all codes work slower on those locations?

Besides this I thought that the Mandelbrot only had 1 fractal dimension, which is an indication of the roughness (Mr Benoit liked to use the word roughness more than fractals, iterations or geometry). How come the left antenna seems more smooth than these images? Is it just my (faulty) perception? Any mathamatical explanation for this (which does not go too deep...) ? Hm, perhaps I should have started another topic.

All disks on the main cardioid have dendrites (antennae) coming out of them.  As you move from the large disk centered at -1, to smaller disks, these antennae become rougher, as they have to encompass more arms (corresponding to the larger periods of orbit of points in these disks).  The left antenna is for the period 2 disk and has the fewest arms, one out and one in, with a hub at about -1.54.  Also, because of the symmetry of the iterating equation, the set (and the left antenna) is symmetric about the horizontal axis.  Taken together, these two ideas suggest that the left antenna would be smoother than the others.

Another approach is to realize that, since the boundary of the Mandelbrot set has a fractal dimension of 2, one would expect everything to get rougher, the deeper you go close to the boundary.  Since the left antenna extends out to -2, it is the furthest away from the "core" of the set, and might be expected to be the least rough.

Here's another one -

(http://www.fractalfreak.com/Images/Negative_thumb.png) (http://www.fractalfreak.com/HQGallery1/Negative.html)

It never ends..

Here's a tutorial and sequence of pictures showing how to approach the cardioid and reveal these lovely cloud digits (or bulbs as I sometimes call them). Any part of the Mandelbrot can be approached this way. Of course, there's no end to this progression. However the compute required grows very rapidly. This hobby is not for the impatient.

(http://www.fractalfreak.com/Images/CardioidZoomSequence/Sequence_1.png)

First image (above) the red arrow indicates the digit of interest, one of the eight cardinal compass points of the Mandelbrot set. Rectangle in white, as for all images below, outlines the region being shown next.. image below (NOTE - the period of the sine wave representing the number of iterations for these escape time 'shaded' images changes (increases , sometimes greatly) from picture to picture in the sequence. This is done to control the increasing complexity of the image. They are all escape time pictures however, despite the magnified image appearing different.)

(http://www.fractalfreak.com/Images/CardioidZoomSequence/Sequence_2.png)

Circle in white - Digit of interest. For this type of zoom, there's a binary decision to make.
Red arrows - We follow two's never ending attempt to reach unity.
Bulbs circled in blue - We must choose one of these two bulbs for the next zoom. This is the binary decision. This process is repeated, until ones patience expires :)
For this progression I'm attempting to select the digit wherein the three largest minibrots, circled in green, have nearly identical areas. As well as overall digit symmetry.
I choose the left bulb, image below

(http://www.fractalfreak.com/Images/CardioidZoomSequence/Sequence_3.png)
If will be noted the three largest minibrots, circled in green, are similar in size, as is the symmetry of this digits arms.

Let's have a closer look, below
(http://www.fractalfreak.com/Images/CardioidZoomSequence/Sequence_4.png)

Again, we must choose between the two digits, circled in blue, avoiding the asymptotes. As per selection criteria enumerated above digit number two is chosen.. below

(http://www.fractalfreak.com/Images/CardioidZoomSequence/Sequence_5.png)
For the next zoom, the left digit is deemed slightly (very slightly) more symmetrical. There's no regular pattern, from my observations, whether to choose the left or right digit for the next sequence. Only visual examination

(http://www.fractalfreak.com/Images/CardioidZoomSequence/Sequence_6.png)

For final digit we choose the right bulb this time - image below.

(http://www.fractalfreak.com/Images/CardioidZoomSequence/Sequence_7.png)

The computational expense of this zoom method is staggering. For the first image a maximum iteration (bailout) of ~500 was required for an accurate census. For the image above, the bailout was 500,000 to attain an accurate approximation of the Mandelbrot set. As can be seen the three largest minibrots (A, B, C) are relatively symmetrical and the cardioid limit is now approaching a straight line, 45 degree angle.