![]() Slightly improved my Brahmabrot technique. Some of the transforms I used in fact need less to even show anything. While often do use 200,2000,20000, it's not always the case. The bailout values you mention were an example by me. You might also want to mess around with prefactors to further control frequencies and phases of the ripples. The swirl transform would then be something like:įor the logarithmic version, just use log(r) in the sin and cos instead of r. There might also be a nice triplex version to this. The formulae I wrote down were the full thing. To get to that from my version, you just need to normalize the wave heigth, mess a bit with the frequencies and add in a time dependency and possibly, to get to a more generic form, a phase.īy the way, the Summoner and the Daemon of Circles both do not require squaring. That's what I was aiming for with my transform. But they illustrated the expected waves in a gif. So I see you liked my naming of that later one. Note, what ever formula you try, the described swirl transforms should simply replace your typical z, rather than the entire equation. Which should make the ripples along the radius be dependend on the logarithmic distance rather than the linear one, so the spiral becomes logarithmic instead of Archimedean. Where f and g would be frequency factors.Īn increase in f would mean more frequent ripples along the radius, while an increase in g would mean more turns. I think there might be some nice variants of it, if you fiddle with the frequencies. The squared Version wasn't symmetric, you say? Weird. I recall finding out about gravity waves back then and there was a Wikipedia image of two neutron stars orbiting each other, generating swirly waves, so I tried to find a way to make such waves myself.) I really love the swirl transform I crafted. So at the very least it's efficient in this way. "Once 20000 is reached, sace results into red channel and stop." "Once 2000 is reached, save results into green channel." "Once 200 is reached, save results into blue channel." So while eating breakfest I rendered tangentbrot is smaller resolution. Oops, after it rendered I slightly moved picture (I renered this in Chaos pro), so it cutted of the bottom. With basic values it were too pixelate, but with slightly less colours and more ambient light there are less pixels. Then colours are by absolute value.Ībs(x+yi)*ei(abs(x+yi)+arg(x+yi)) squared +c didn't wanted to generate simmetric picture, but with real modulus it become simmetric. Here ambient light is negative, and colour value is added to it. Tested some formulas and picked what looked best. This one is reasonably fast even on my very old old pentium 2. And probably alsou colour calculation by 3 iteration lenghts makes it 3x slower. ![]() Alsou if you iterate point twice as described in original buddhabrot algorithm, it makes it slow. So I didn't throw out any orbits, what saves some calculation time, but it's not quite an buddhabrot or antibuddhabrot ). If you iterate and throw out escaping orbits, you have antibuddhabrot, and picture builts much faster, but still some orbits are iterated but not used. If you calculate buddhabrot proper you pick random points, iterate, and throw out non escaping orbits and picture builts up very slowly. That being said, I'd love to see your versions for comparison. (notably all the points where x tan x = 0, which happens where ever tan x = 0) Likely a result of the tangens being a exponential and rational function.Ī proper bailout area likely is relatively complex, since tan repeats infinitely and thus there are infinitely many regions outside of any given circle that would still converge. I already noticed that it essentially includes features of polynomial MSets of every order. I'd love to see more experimentation with that MSet. It may very well be that, if you have a different bailout strategy, you get quite a different result. I noticed in later experiments that you can significantly change the results by discarding values that are inappropriate for the given render. Note, though, that what you see is a fairly low-quality image that is relatively heavily post-processed to recduce noise and such. I wonder what would be the "actual" formula for it. Not the typical radius 2 but more like radius 32 or something. It's very likely that I simply used a circular region of big radius. ![]() I can't recall what exact bailout settings I used and such.
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