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Following a suggestion from DarkBeam i modified the reciprocal formula a bit to limit artifacts.

The results are changing with bigger limits, but are still unique enough to use it instead.

Here is a pic with limiter = 0.6, took only about 3 minutes with stepwidth limiter of 1:
(reciprocalX2 + sierpinski)

(http://nocache-nocookies.digitalgott.com/gallery/5/1127_12_02_11_9_45_29.jpeg)

Would a reciprocalY or reciprocalZ be possible?
If so, would they be useful?

If Jesse don't write reciprocal y z i'll do by myself. It is a menace :lol:

Only if you write a reciprocal R too, just my menace  :dink:

Sphereinv is a reciprocal r. :D Already done :banana:

From sphereinv description;
x', y', z' => Translate + scaling (by radius) of x, y, z with given params.
Then, defined Rho = (x'*x'+y'*y'+z'*z'), <- = R
x'' = x'/Rho
y'' = y'/Rho
z'' = z'/Rho

 :dink:

uhm, youre absolutely right... dividing by the sqr.

But a little tip should be ok, because dividing is much slower than multiplication:
compute the reciprocal of Rho and multiplicate 3 times, fld1, fdivrp to do the reciprocal value.
Just in case you had not done so, i didnt looked at the source.

Keep up your good work!  :)

But in the end you have to divide in every case :hmh: ... Where is the optimization?

Another question

You divide by y+epsilon. But I meant;
compare y by epsilon
if y<epsilon, cutoff.
;)

Instead of:
x'' = x'/Rho
y'' = y'/Rho
z'' = z'/Rho

You do:
Rho = 1 / Rho    //or include it in the step before
x'' = x'*Rho
y'' = y'*Rho
z'' = z'*Rho

So you have only 1 division instead of 3.


I know, that is a bit different version.
Did not tried your version, dunno what might be better.  Just do it like you want and we have more options.  :)


Forgot:
in my formula there is a little bug, if you use negative limiter values:  i used 'or' for the sign function and not 'xor', but that affects not very much.
And it makes no difference on positive values, so it is not urgent to change it.  Just if you want to copy it...

I need your help for  coding my first formula ... A 4d extension of Barnsley but too bad don't work. :) tomorrow I will send

Here they are, gives new nice possibilities in combination with the sierpinski for example!

The limiter instantly gives me animation ideas :) Thanks Jesse!

Ohw yeah very nice! The possibilities got infiniter once again  :dink: