can someone confirm correctness of uf5 mandelbulb formula?

[DarkBeam]

And of course it's completely different from the standard

[David Makin]

"Makin" is back - but a little tired....will check tomorrow evening - oops *this* evening....though after just going for a family wedding in Moray (Scotland) even closer family arrive here from Surrey today at around 4pm......

Of course you could just use the code from my mmf wip formula - in fact I think you could just use the formula as I think it allows cutting planes (though don't rely on that as I'm falling asleep).

http://www.fractalforums.com/mandelbulb-implementation/update-to-the-mmf-wip-formula-for-ultra-fractal/

[cKleinhuis]

the reason for this tutorial is to develop the mandelbulb formula from scratch, any hints
on compacting the code are welcome, but it shall serve as :
*how-to write formulas for ultrafractal,
*what is polar exponentiation
*what is spherical exponentiation
*and it shall be developed from scratch from the standard mandelbrot formula
* should serve as well as general introduction into fractal stuff and what we do here on the forums
* invite people to experiment with the formula editors
* general fractal math tutorial

it will be georgeous, and is planned as one of the first tvshow entries, it will consist of nearly 10 parts, and i talk something, and then switching to the ultrafractal screen... stay tuned...

any hints and comments are welcome,as well as hinting me where to make changes for the cosine/sine mandelbulb variant ...


and in fact, i still have a question:

WHY IS THE ANGLE CALCULATION FOR THE SECOND ANGLE NOT USING ATAN2 FUNCTION ? !?
in my eyes it would be much simpler to adopt the atan2 function to just use another pair of coordinates, but why the heck it is calculated by "asin(z/r)" ?!?!?!

[DarkBeam]

WHY IS THE ANGLE CALCULATION FOR THE SECOND ANGLE NOT USING ATAN2 FUNCTION ? !?
in my eyes it would be much simpler to adopt the atan2 function to just use another pair of coordinates, but why the heck it is calculated by "asin(z/r)" ?!?!?!

You can convert asin() to atan2(); I did that in my implementation, as arcsin() simply does not exist in f.p. assembly!

See General formula help.

arcsin(z/r) = atan2(z, hypot(x,y))  

hypot(x,y) = sqrt(x*x + y*y)

asin(z/r) = azimuth angle

[DarkBeam]

btw Mandelbulb3d has a 2d mode, that you can explore using the rotation buttons, spin it all around!

[David Makin]

WHY IS THE ANGLE CALCULATION FOR THE SECOND ANGLE NOT USING ATAN2 FUNCTION ? !?
in my eyes it would be much simpler to adopt the atan2 function to just use another pair of coordinates, but why the heck it is calculated by "asin(z/r)" ?!?!?!

Because you need r anyway (usually) and asin (on fpu) is considerably faster than atan2

Sorry still haven't had time to check the code - things are still hectic here as although I'm back home from Scotland my brother and family are here at the moment (Steve, Christine, Max, Zoe, Yasmine and George) plus I'm trying to process all the pics I took while in Scotland among other things....

[cKleinhuis]

@darkbeam, me: "ah, great that makes sense thank you for clarification ... although i cant explain it with my own words yet i am happy", right the mandelbulb3d has a 2d mode, but i never understood how to correctly use it, and what 3d picture results from it but just because i didnt spent too much time to find it out ...
but i will do it in ultrafractal, because i want to just show properties of fractal formulas in general, and ultrafractal in special... and at the end we will shortly watch mandelbulb3d and mandelbulber do their beautiful work ...

@dave take your time, i am interested what you say about how correct it is, in general but your uf5 expertise is also wanted,
 e.g. returning z value only in the iteration loop could lead to not so nice coloring problems,  or how to make "power" variable defined in base class a float, or at least hide it from display 

[cKleinhuis]

My holy Saint Spaghetti Codes!!! I tried your formula, I must say I would be very curious to see how it's rendered in 3D...
I was able to run it only after creating an ulb. Another complication!
But I can not understand a row of your damnedly complicated code! The "real" formula is far less complicated than that... 5/6 rows of code and no need of all that commentary.   Please think simpler! Thanks!

lol, are you real ?
it shall serve as a tutorial, and every line that stands there has to fulfil a certain purpose or has to get lost ... ....
and i used some nasty copy&paste code, that will be discussed in the tutorial as well, and that it is clearly not a speed
optimized code is known to me as well ( nasty function calls ) but this structure allows easy understanding for not so
fractal-assembler-affine people ...

problem is that many many parts of the code just deal with some shortcomings that ultrafractal parser has ... e.g. i dont know how to create a complex number on the fly i needed some time to find out that x+flip(y) has to be used to make a complex number out of x/y

and some parts are declaring and using local variables for storing the iteration inbetween results hence uf5 just deals with complex numbers in the iter loop, and i wanted to store all parts of the number, and not only the z ... just to make things even clearer what is happening ...

and for sure i am going to switch start values at the start of the tutorial to show how to create julia sets

[David Makin]

or how to make "power" variable defined in base class a float, or at least hide it from display  

In the derived class have a parameter of the same name and type as the one in the parent class but with "visible=false".

[cKleinhuis]

ah, thanks, what about casting/creating complex numbers on the fly ?
i would like to return it this way:
return (real,imag)
i am working on the steps of the formula, commenting every line, and parameter
will let you review it ....