File:Multibrot Shape Forming

Description
My deepest and longest zoom yet!

Final magnification: 10^150.

To start, I need a minibrot to get my embedded Julia sets from. The minibrot has to be deep enough so there isn't much distortion. (This also causes the layers to be more spread apart.) I chose the minibrot at 0:18, at a size of one ten billionth the size of the original.

By zooming near the elephant valley, we soon get an embedded Julia set at 0:26. It has three-fold symmetry because this is the power-three multibrot. There are also the 9-fold Julia set, and the 27-fold, and the 81-fold, and the 243-fold, so on, at 0:28, eventually leading to the minibrot. But that's not where we're zooming.

Next, I zoom into the edge of the 9-fold Julia set. Notice that every C-roll is made up of three smaller C-rolls! How cute!

Zooming into the edge forms the shape seen at 0:36. That right there is actually three 9-fold Julia sets FUSED TOGETHER. They're fused because I zoomed into the interior of the first 9-fold Julia set. I call this shape a 3-star because it's a star with 3 legs.

Then, at 0:38, there's another star, but wait, it's got 9 legs instead of 3. Whoa! Of course, there's also the 27-leggged star and 81-legged star and so on, surrounding the minibrot you see at 0:39. But once again, we are not zooming there.

So I zoom into the armpit of the 9-star. The result of that is 3 fused 9-stars, visible at 1:12, 1:27, 1:37, 1:47, barely 2:01, barely 2:14, and 2:31.

At 0:45, I zoom right by the armpit of the 3-star, but not inside of it. That results in three 3-stars, but NOT fused. They are very distorted. You can see them at 1:14, 1:39, 1:49 and 2:34.

At 0:55, I zoom right by a 9-fold Julia set, not inside of it. The result, as you can probably guess, is 3 not-fused 9-fold Julia sets. They're seen at 1:42, 1:52 and 2:41.

At 1:05, I zoom into a spot halfway down a 3-star's leg. The shape formed is seen at 1:56 and 2:48. It looks like a weird triangle with Y's growing from each side. Ugh.

At 1:14, I zoom near the three unfused 3-stars. As you'd expect, I get 3 groups of 3 non-fused 3-stars. Seen at 2:54.

At 1:27, there's 3 fused 9-stars again. What fun. I decide to zoom into a leg of one of the 9-stars. The shape formed is good, I guess, and it's at 3:03. There are 3 fused groups of 3 fused 9-stars. It's surprisingly square for this multibrot set.

From 1:30 to 1:34, I just decided to zoom into the ends of the legs of three 3-stars. You can see the shapes formed at 3:06. They look like circles with 3 Y's growing out of it. And there are three of them embedded in one other. Obviously.

At 1:42, you can see three non-fused 9-fold Julia sets. I zoom into one of the three. The result? 3:14. The one Julia set I zoomed into is huge now, and the other two are tripled around its edged. Yay!

There is the weird triangle with Y's growing out of it at 1:56. Zooming into one of the triangle's "corners" forms the shape at 3:23. You can see there are 3 of the shape fused together!

At 2:00, a 27-fold Julia set appears and I zoom into one of its many spirals. (There are actually an infinite number of them.) It is a very pretty spiral indeed, but the iterations get pretty high in there so I stop at 2:09. The result is nice. It's at 3:26 to 3:31.

2:15. I'm zooming into the ends of the legs of a 9-star. Result at 3:35. Actually, very similar to the shape at 2:31, except for a few differences. One, the place where they are fused is thinner, mostly because where I zoomed was thinner - the end of a leg instead of the armpit. Also, each fused star only has eight legs this time. The ninth is the one connecting it to the other two. Both understandable.

At last, at 2:18, I'm centering in on a minibrot. No more detours. I keep zooming into the center until I find that minibrot. Because this is a third-power Multibrot set, zooming into the minibrot will take up one third of the zoom. That's true: the zoom is 150 powers of ten, and 50 of them are spent centering in on the minibrot!

Everything in the zoom ever starts to repeat at 2:18, but tripled. That's crazy. There's 3-fold symmetry.

It starts again at 3:38, but times nine. Now everything has nine-fold symmetry! (4:04 is my favorite part.)

It starts again at 4:08, but times 27. Now everything has 27-fold symmetry.

It starts again at 4:16, but times 81. Now everything had 81-fold symmetry.

So on. It repeats infinitely as it approaches the minibrot at 4:22.

Maximum iterations: 400,000. Should have been higher, you can see that at 4:22.

5 days were spent rendering.

Music is "Hypnothis" by Kevin MacLeod http://http://incompetech.com/