Bild:3D Julia-set (IFS 001).jpg
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3D_Julia-set_(IFS_001).jpg (95 kB, MIME-Typ: image/jpeg)
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Julia set, a fractal, here in three dimensions. The image was created from using a "iterated function system". This is not a quaternion - only three parameters; x, y, z was used in the reversed formula Z = sqrt(Z − C). In 2D the root function rotates to half the previous angle and scales to the root of the previous length. I developed a method to do this using three parameters, (see formula in C-code below).
See also:
External link:
- Download a demo program that creates images like this, (and more) from: 3djulia.htm
All freaktal images are from self-written tools. Linear fractals from my : "3D IFS studio" and "3D DTIFS" (dragon trees), non-linear IFS from "3D RJIFS" (3D rev Julia). |
See also: Solkoll & Solkoll 2D
[edit] Source-code:
C-code snippet:
// Notes:
// All variables are declared as "float" or "double". // x, y, z is the 3D variable "Z". // a, b, c is the 3D constant "C" (the Julia-coordinate).
// RND is a random float in the range 0 - 1, define it like this: // #define RND ( ( float ) rand ( ) / RAND_MAX )
// Here the function:
x -= a;
y -= b;
z -= c;
length = sqrtl ( x*x + y*y + z*z );
root = sqrtl ( length );
if ( length == fabsl ( x ) )
{
if ( x < 0.0f )
{
angle = RND * pi * 2.0f;
y = cosl ( angle ) * root;
z = sinl ( angle ) * root;
x = 0.0f;
}
else
{
x = root;
}
}
else if ( length > 0.0f )
{
x = ( ( x - length ) / 2.0f ) + length;
y = y / 2.0f;
z = z / 2.0f;
length = root / sqrtl ( x*x + y*y + z*z );
x *= length;
y *= length;
z *= length;
}
// This is the IFS: randomly select any of the two roots :)
if ( int ( RND * 2 ) )
{
x = - x;
y = - y;
z = - z;
}
If you like to get more information about this function? then write at: User talk:Solkoll or drop me a wikimail.
Dateiverweise
Die folgenden Artikel benutzen dieses Bild:
