Image:3D Julia-set (IFS 001).jpg

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:

• w:en:Julia set
• w:en:Iterated function system

External link:

• Download a demo program that creates images like this, (and more) from: 3djulia.htm

Image: User:Solkoll. This image has been released into the public domain by its author, Solkoll. This applies worldwide. In some countries this may not be legally possible; if so: Solkoll grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. العربية | Български | Deutsch | Ελληνικά | English | Español | Français | Italiano | 日本語 | 한국어 | Polski | Русский | Српски / Srpski | Svenska | தமிழ் | Українська | ‪中文(繁體)‬ | ‪中文(简体)‬  +/- More 3D fractals from my tool: Image:3D Cantor set.jpg Image:3D Julia-set (IFS 001).jpg Image:Dragon trees.jpg Image:Fractal tree (Plate b - 1).jpg Image:Fractal tree (Plate b - 2).jpg Image:Fractal tree (Plate b - 3).jpg Image:Fractal weeds.jpg Image:Harter-Heighways dragon curve (3D twist).jpg Image:Heavy Lévy.jpg Image:Julia set (reversed formula 3D).jpg Image:Lévy's C curve (3D-goggles).jpg Image:Lévy C curve (3D-twist).jpg Image:Menger sponge (IFS).jpg Image:Menger sponge (Level 1-4).jpg Image:Sierpinski pyramid.jpg Image:Sierpinski tetrahedron.jpg Image:Sierpinski tetrahedron (Detail).jpg 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.

La page ci-dessous contient cette image :

• Ensemble de Julia