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The making of Magnum Opus X Part 1



This deviation pertains to my "Magnum Opus X" fractal.
I have named it "Magnum Opus" which is Latin for "Great Work". I hope it is not egotistical to suggest such a name, but the amount of effort involved in discovering such a formation is greater and at a vastly deeper zoom level than any other fractal project I have worked on thus far.

Basically, this represents my long term goal of creating an "X made up of Xs, which are made up of smaller Xs." First off, the inspiration for this technique started off with "Metaphase", a render which supposedly showcased the origin of life, represented by the appearance of a cell which contained two small X-chromosomes. The original stills and a video rendering can be found at HPDZ.net

This inspired my 2009 piece, "XX Reactor Core" [link] which basically consists of a large "X made up of smaller Xs". Over time, I pondered whether it was possible to continue this process a step further. If "Reactor Core" could be represented as X^X, then maybe it was possible to produce a much deeper render consisting of these X^X formations arranged into the shape of a much larger "X". A moth later, I discovered such a formation, but it didn't really strike me as attractive, even after countless tweaks to the color palette. My first attempt at choosing a new zoom path specifically to shorten the zoom and iteration depths as much as possible, yielded a result which was visually not very bold or interesting. For a while, I gave up on the idea. It is interesting to note that the prototype render as well as all three of the 2011 render tests each contain exactly 1024 X chromosomes. The prototype had 32 large X^X formations, each consisting of 32 smaller X formations. I thought that the symmetry involved in 32*32 would work, but for some reason, it just didn't.

Later, through creative exploration, starting with Point #1 on the 32X location, I finally derived a XXX formation with each X made up of smaller Xs, at about 1764 zoom levels. See "XXX Cold Fusion" [link] I had discovered the "odd" method of making X fractal! Instead of waiting for "X" and zooming into the side, I zoomed off the side of the "I" formation instead. Then when I get two "I" shapes, I zoom into the center of one of the two arms, which after another periodic doubling, results in a central "X" shape with two broken "I" fragments on either side. Zoom to the center of the fragment again to produce a 3X formation with additional broken fragments on the side. This was carried over to produce a 7X formation, see "X7 Hot Fusion" [link] which carried the effect another level. Although I rendered it in October 2010, I did not post it on deviantart until November 2011. Doubling the "Hot Fusion" fractal by following into the deep center produced "Test #1". The arms of the fractal looked really nice, but because the center of the 7(X^X) formation was an "X" shape, the resulting image after zooming into the centroid and doubling it looks more like an 8-armed starfish or an Octopus. This kind of ruined the effect.

My next attempt was to produce the desired (X^X)^X formation by employing the even method. For the even method, I started at Point #2 of the original "Reactor Core" formation, and zoomed in on a spiral which was located three Xs away from the centroid rather than six Xs away. The X formations are still skewed for artistic license, but noticeably less so than with Test #1. I zoom in on the closest Julia midget within the spiral, because I want each doubling to look identical. When I finally get to the 8(X^X) formation, I zoom into the centroid to double it. But the "X" formation really draws the eyes into the center of the image, and the inflection point that I chose for the center is visually uninteresting. So once again, the result is not quite what I wanted.

For the third attempt, a flash of genius hit me. During Test #1, the center formation was eight-sided because the central figure that I zoomed into had four arms. So, how could I duplicate the effect with a four-sided midget in the center rather than eight? Simple. On the 3(X^X) formation, the bent fragment at the end of the feature is mostly similar to the 32X formation which doubles to form "Reactor Core". If I use the even method to zoom past the last "X" chromosome on the bent arm, it will essentially double to form a long slash mark in the center of the 7(X^X) formation, instead of another (X^X) shape. Double this again, and I get the giant (X^X) formation in the center of "Magnum Opus". A 64X long arm present in the center of the "XXX/XXX" formation doubles to form a huge (X^X) formation with 128 little X chromosomes. Thus, "Magnum Opus X" has 128 Xs in the central formation, 64 Xs in each of the 12 (X^X)s present within the arms, 64 * 12 = 768, and 32 Xs in each of the bent arms at the end of each leg, 32 * 4 = 128. So 128 + 768 + 128 = 1024 = 2^10. As always in the Mandelbrot set, the number of features always adds up to a whole number exponent of 2. With four arms per each X formation, that's 4096 arms total, or 2^12!

Because I felt the tilt effect was less severe on Test #2, and since the odd spirals do not have arms extending out of them, I rewound the zoom all the way back to the original 32X formation and chose a spiral to start off three Xs away from the center at Point #3, rather than six as in Point #1. This turned out in my advantage, as the asymmetric effect remained very subtle, especially since the central (X^X) formation at the center of the "Magnum Opus" object is by nature also asymmetric.

This is part 1 of 2. My next showcase will feature the exact road map leading up to "Magnum Opus X" zoom path, detailing every point at which I detour away from the centroid. Stay tuned...

Wow, that was quite a mouthful, if you've actually taken the time to read all the text thus far! Comments, favs, and Llama badges appreciated!
Image size
1280x1280px 2.26 MB
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