Perturbation for z^3 + c

[Dinkydau]

This is the same kind of zoom method as was used for "Mandelbrot extremism", now applied on the 3rd degree Mandelbrot set. Thanks to Kalles Fraktaler for implementing perturbation for this fractal! I zoomed very rough and fast because I just wanted to see what it would look like. I think the randomness in this caused by the rough zooming actually turned out to be pretty nice. Note how low the magnification is. It's because shapes are much closer to each other in the 3rd power Mandelbrot set. It really makes a huge difference and it does actually make it easier to explore. This render took one hour, while the equivalent of this shape in the standard Mandelbrot set took a day. I guess you're in luck if you like 3-fold symmetry.

You can click the image to view the original image on deviantart, at a resolution of 4000×2250.

Coordinates:

Code:

Re = -0.2754540800037159147988012245766986989506972491540947467271925358857405817448058964117420846278941156587617485329288010167448891783709099583442697498572354593057010236876313021869958635
Im = -1.2523370716385274901529790243876410633562501379385716110360708549830384058605721976908813696660026605671793807058250599438911013691966653022152293796500461847740317144649934836264947449

Magnification:
2^511
6.70390396496E153

[Kalles Fraktaler]

Wow beautiful.

But the 2nd power equivalent is not your +e900 location right?

My findings so far is that the final minibrot in the 3rd degree set is 1/3 away, compared to 1/2 away in the standard Mandelbrot. If you want to make a movie to e100 you need to start center at e67 instead of e50.
That is denser, but not so much denser...?

[Dinkydau]

Thanks

Indeed this is (somewhat) equivalent to the e900 location and those fractions are true as well. For every morphing in the standard Mandelbrot set, the next shape is 1/2 further, while in the 3rd degree Mandelbrot set it's 1/3 further. At first this doesn't make much difference, but eventually it does. The first julia set is at a depth of 2^18 for both fractals. From then on, there starts to be a difference. I think this took 12 morphings to make, so seen from the starting point that is about
(4/3)^12 = 31,56929...
times further down.

In the standard mandelbrot set, that would be
(3/2)^12 = 129,74633...
times further down.

The depth increases stack, so the deeper you go, the bigger the difference gets. The depth of this is E153, so if the factor 4,2 would be correct, the equivalent shape in z^2 would be at a depth of E4,2*E153 = E642,6. That's not enough, but if you do that times 1,5 you get something between 900 and 1000, so the amount of morphings in this location is probably one less, which makes the difference look more extreme than it is.

There is another factor, though, because the depth increase is not always exactly those fractions, which makes it much more complicated to make accurate calculations. In some situations, the actual depth may be less (but not more). The minibrot at the center of one of the trees in the shape above is closer by than the minibrot you would get by going into one of the thin lines. That's because for every tree created, already part of the zoom path has been done on the way to get to the tree.

[Pauldelbrot]

Thanks

Indeed this is (somewhat) equivalent to the e900 location and those fractions are true as well. For every morphing in the standard Mandelbrot set, the next shape is 1/2 further, while in the 3rd degree Mandelbrot set it's 1/3 further. At first this doesn't make much difference, but eventually it does. The first julia set is at a depth of 2^18 for both fractals. From then on, there starts to be a difference. I think this took 12 morphings to make, so seen from the starting point that is about
(4/3)^12 = 31,56929...
times further down.

In the standard mandelbrot set, that would be
(3/2)^12 = 129,74633...
times further down.

The depth increases stack, so the deeper you go, the bigger the difference gets. The depth of this is E153, so if the factor 4,2 would be correct,

Do you mean four point two? If so, something's gone wonky with the punctuation marks in your post, though other periods such as at the ends of sentences and in ellipses seem to be unaffected.

[Dinkydau]

In this particular post, a comma was used for decimals. Thanks for making me aware of it

[Kalles Fraktaler]

In this particular post, a comma was used for decimals. Thanks for making me aware of it

European vs North American...

A hundred thousand can in Sweden be written as 100.000,00
And in America as 100,000.00

[SeryZone]

European vs North American...

A hundred thousand can in Sweden be written as 100.000,00
And in America as 100,000.00

Yes, we use IntPart,Floorpart