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Hi all,

   I was curious to see what happens if you replace e^2ln(z)+c with e^(ln(z))2. Here's the overall shape:

(http://i624.photobucket.com/albums/tt323/schlega1/fractals/full2.png)

The crest on it's head:
(http://i624.photobucket.com/albums/tt323/schlega1/fractals/fullzoom10.png)

(http://i624.photobucket.com/albums/tt323/schlega1/fractals/fullzoom1.png)

The tip of it's abdomen:
(http://i624.photobucket.com/albums/tt323/schlega1/fractals/fullzoom2.png)

The mouth:
(http://i624.photobucket.com/albums/tt323/schlega1/fractals/fullzoom3.png)

http://www.youtube.com/v/5I2KhmT_Ybo&hl=en_US&fs=1&rel=0

yet another great variation of the default formulae :D

That's one of the coolest Mandelbrot variations I've ever seen (that still retain its form, to some extent). Many others involve things like the Mandelbrot with big chunks attached at every Misiurwecz point, or just being a distorted version of a multibrot, etc...

This one is very original. I would love to see a parameter shift of e^(ln(x)*(2*n+ln(x)*(1-n))) from n=1 (the default Mandelbrot) to n=0 (this one). I think parameter animations always provide a new layer of insight into how a fractal "gets" its shape.  :D

Thanks, guys. I'm uploading that interpolation right now, but I did it in 1080p and I have a slow connection. In about 10 hours, it'll be up.

Also on the to do list:
-Make an animation using z^{2n(ln(z))(1-n)}
-Explore z^a(ln(z))b+c
-Use the triplex formulas for exp(z) and ln(z) to make a beetlebulb.

I like it ! *hugs*  ;D

*hugs ker2x*

Youtube didn't like the uncompressed HD version, so I had to reduce the quality, but it's up now.

http://www.youtube.com/watch?v=W7dFONTB0kk

Tantalizing! What I wouldn't give for a computer I could explore that on....  ;D

Here's an alternate interpolation:

http://www.youtube.com/watch?v=7mwxluQo6iQ

This is what the triplex definitions of exp and log do:
(http://i624.photobucket.com/albums/tt323/schlega1/fractals/truebeetlebulb.png)

The spew would probably be reduced with higher iterations, but my computer isn't fast enough to explore it in detail.

Here's an exponentialish version:

expish(x,y,z) = exp(x)*(cos(y)cos(z),sin(y)*cos(z), sin(z)),
logish(x,y,z) = (ln(x²+y²+z²),atan2(x+iy),asin(z/r))
http://www.youtube.com/watch?v=Yip3BDZF_Wc

doesn't look that buggy anymore, now.
But still very nice :D

Which definition of exp and log did you use in the other image?
Whoa, it looks like the bug didn't survive that xD

I'm guessing he used the Maclaurin series for exponentiation/logarithms... you know, 1+z+z^2 / 2 + z^3 / 6 + z^4 / 24....

I used the analytic formulas that were derived in the triplex algebra thread, which came from the series definition.

ah, that one :)
A very complex formula.
Must have taken forever to even do such a low-iter version.

Yeah, it took about half an hour for that picture. And now I have to do it again because I found a bug in the code.  :sad1:

Here's what the video should have looked like:

http://www.youtube.com/watch?v=2yjQnwBgi7s

The long formulas looked even less interesting after I fixed the bug. Have some Julia sets instead.
http://www.youtube.com/watch?v=NI5-FOksWGs

Oh, I like the Julias. How is that moving through the plane? In a line? If it's a line it's an interesting one, all that switching between connected/disconnected Julias.

still nice but lol:
Yet another example for bugs making it more interesting.
What tells us that for life?
Living without error = Being boring or feeling bored.

I just picked some points outside of the mandelbrot type and let Chaospro interpolate between them. I'm trying to write a program that will detect a path along the boundary and animate those Julias, but I'm having some trouble with it.


Quite true  ;D

What *is* the error? It sounds interesting!   ;D

Wow, detecting a path along the boundary? That sounds really tricky... Good luck with that, I'd love to see the result!

In my squaring function, I had x²+y²+z² where I meant to put x²+y².


Thanks. If I ever get it working you will!

I didn't get the results I wanted, but sorting boundary points by angle seems good enough for now.

http://www.youtube.com/watch?v=XKJLDDMudpQ

Very nice! Looks like you're wobbling back and forth across the boundary. Incidentally, you might want to slow it down a little--sometimes it changes so quickly I don't have time to spot it! Actually, that might just be a problem with crossing the border in general.

Here is a quaternion implementation for Mandelbulb. Due to the formula complexity, takes ages to render even if the size is 200x200 :-\


Mandelbulb3Dv16{
N....UA....m....w....2....U0AShtAEK7.H5bvWPNTI3ElgrfaBpjqzPVnfjlJc0BzKQepkE3RW.k
................................pYWGHo8/Xz1........A./..................y.2.....
................/ME//....6kVM...82....E2.....IrqizNQX7tD...........c./...w1....U
z.EnAnQD..../..GVf53iSIozAnAnAnAnAyjaNaNaNaNKz1..................y1...sD...../..
.wHnAnQDPTzMS4rMGy1..........U4FWpEfUsfjyEeJWZXfcrnqrDablBaYzC6QPfEfUsfDlToq8o86
yufxg7K1h0WjyK23NnNQX7tj......o60.....................sD..kz0...................
.............................UJRR4.wppN.6OLb/.mRR4.irpN.EVLb/UCSR4..............
................E..........U..6.4/...61...EB....I....U3....3....m....IX1...UiePI
..kI4ydelyjeYFnzTeOgzf8Nos8.1c..zzzz.MQizccZWGyD7EdGkxmWcz1...........k.8.kXWF1.
QvM93P58iz9GMmnWK2zwz0..........ZM1IyDL7O.kjthne8d.kzm0Ju0SpJhyD.m1wnEqe5zP.FcEz
4NqQ.6UkKZMxkayjtodIWOorVyvkhw1ZBGouzKF.8wDJ030.8B6ewXyKUzXbbFpvWtc6.l4zvm1FFj1E
3EU00U5GZ.EBK2Ean0HxzGPFm0nvAI.kddPEmLBlt.2...uBZ.EHVM/.zzFoTu2.cxo7.szDnueM.g5P
D/EzTt6Ul/kF.V1.Qs5crI0.B3W3..bTUSH7.oI6K..ly/uBZ.EHVM/.Mw5crI0.B3W3.kqTUSH7.oI6
K..kz/uBZ.EHVM/....crI0.zzFoTu2.yzngi84.xzZX.45..IaMUELNoJ46YJ46XVa9e/rN..UOkR4.
E....I....E.....I.........kLAxqNoE2...pPrJaQ....................................
...................../........................................zD........kz1.....
...wz.........zD........kz1.....................................................
.....................2.....3....7....2JRVF5IjR5.................................
...............................E........................................kz1.....
...wz.........zD........kz1.....................................................
................................/....E/.........TJ2SkF1F........................
........................................U.2.....................................
................................................................................
..........................................E.....I....A....kLVF4N1/..............
...................................................wz.........zD........kz1.....
................................................................................
.....................................................2.....3....2....wpIX34PdtqN
klKRn/......................................................../E........E.2.....
...2./......../E................................................................
................................................................}

Hey, it's been a while since I've been here.

DarkBeam, I tried to look at your quaternion implementation, but it just says "Error, formula option is not valid." Am I doing something wrong?