END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

Don't forget those formulas

; --- Samuel Monnier ducks. Never escapes (all inside)
z = real(z) + flip(abs(imag(z)))
z = log(z+pixel)

; --- Barnsley generalized
; --- default values re1=1, re2=0, re3=0, fac1=(1,0), fac2=(0,0), fac3=(0,0)
; symmode=false, bartype=0
if bartype==1
condition = real(z)*imag(c)*re1 + imag(z)*real(c)*re2
else
condition = real(z)*re1 + imag(z)*re2
endif
c = pixel

if condition  > re3
z = (z + fac1) * c + fac2
else
if symmode
c= conj(pixel)
endif
z = (z - fac1) * c + fac3
endif

If you need others ask
flip(z)=z*(0,1)
conj(z)=real(z) + flip(-imag(z))

This is the UF public database, you can also pick what you need.

http://formulas.ultrafractal.com/cgi/formuladb?browse

Let me step in until Luca returns . . .

No!!! Easy handling of complex numbers is important for most traditional formulas.

If you must use only reals, here's a way to deal with the complex logarithm function for the ducks formula [I think ].

Suppose z = (x, y) is complex. 
Let r = sqrt(x*x + y*y) and t = atan2(y, x). 
Then log(z) = (log(r), t).

Note 1: log(r) represents the usual natural logarithm operating on reals.
Note 2: The complex logarithm function isn't uniquely defined, but this method should provide the principal value.

Supporting links:
Principal value of the complex logarithm
Polar form of a complex number
Definition of atan2

Hey guys, don't be so upset! 

I think I know what I'm doing, just wanted a little help with log function, so thank you Ken!

This is not a very "traditional formula" software, and also I don't want to include a crazy amount of formulas, neither a lot of variations.
I want to do something a bit different, since, as Luca said well, there are plenty of freeware fractal programs available for traditional formulas and well known 2D fractals. I stated before that there will be a very limited amount of formulas availaible, but the way of doing combinations should make a good variety of results.

Also this isn't C++, Luca. It's VB.NET, so optimizing for speed will be very important. A while ago I tried using a complex class, just for Mandelbrot, when I wrote a very rudimentary render for "KaliLinComb" (before Jesse's implementation), and the perfomance was not good (I know, I know... I should use C++)

Let's see what happens... For the moment, I'm dealing with some issues in that DataGridView control, but I think I'm almost winning the battle.

Thanks for comments, I really appreciate them!

What about this?

Or maybe this

Why you fight against the milestones of informatics?
I used Vb many times. Vb uses massively dlls and is the slowest language ever, whenever you need speed you lose your time
The only fast language is C, afaik, that naturally supports assembly and you can obtain awesomely fast routines
I tried to write a Win program in pure C but create an interface in C is too time consuming

Didn't have much time today for coding, but thanks to Ken (and in spite of Luca's discouragement) I already implemented Ducks using only real variables with good results. I ran a test with a 2-color coloring method, just to check if patterns are right, and they are indeed
The original non-antialiased image is 3712 x 1500 pixels, and the rendering time was 45 seconds on my Phenom 9550. 
The number of iterations used for the formula were 25.



I think I can do some more optimization, tough

Nice work, Kali!


Visual Basic is quite slow. There are some very fast basic compilers such as Powerbasic (for Windows) and Purebasic(for Windows,Mac and Linux)  These are not free however but produce fast and small executables. There is also a basic to c compiler bcx ( windows freeware).


Powerbasic and bcx use qbasic like syntax. If you also want to learn C then bcx is your choice since it ouputs c code. Purebasic outputs fasm asm code. I personally have used Powerbasic (since 1997)  but it is quite expensive.

http://bcx-basic.sourceforge.net/

So C is not the only fast language...