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Hadn't introduced some of formulas to public. Consider this being like both wikipedia article and forum post ;)

After an artistic suggestion I tried to make house generating hybrid. Few folds, _Amazingbox with no spherefold and menger sponge and unit vector addition took house like shapes but not quite so.
The greatest problem were that all of the houses are made of rectangles but menger sponge and folds generates squares.

Without any knowledge KIFS or how menger sponge works I just took MengerSmt.m3f code by Luca Gen and modified until it generated rectangle based shapes.

Folding:

Code:

//fold
x := x + abs(x- FoldX) - abs(x+ FoldX) ; 
y := y + abs(y- FoldY) - abs(y+ FoldY) ;
z := z + abs(z- FoldZ) - abs(z+ FoldZ) ;

x := x + abs(x- FoldX) - abs(x+ FoldX) ; 
y := y + abs(y- FoldY) - abs(y+ FoldY) ;
z := z + abs(z- Foldz) - abs(z+ Foldz) ;

Seperate values for x,y,z axis allows both to strech and multiply in needed direction. Menger Cube is single storey and each fold adds 2 storeys. Not shure where I got this fold, but this is one operation faster than usual boxfold.

STart of Menger sponge by Knighty:

Code:

x := abs(x + AdditionX ); 
y := abs(y + AdditionY );
z := abs(z + AdditionZ );

The fractal don't have mandelbrot/julia sets and the mandelbrot set of menger sponge probably isn't meaningfull. But here is julia variable (0,0,0). It moves houses around and can stick pairs of two together.

Code:

/// not shure how this works
//  modified Menger code taken from Luca GN formula MengerSmt
  scale1 := scale -1;
  scale2 := scale1/scale;


t:=x-y; 
t:= 0.5*(t-abs(t + DomoXY) );
x:=x-t ; 
y:= y+t ;

t:=x-z; 
t:= 0.5*(t-abs(t + DomoXZ));
x:=x-t;
z:= z+t;

t:=y-z;
t:= 0.5*(t-abs(t +DomoYZ));
y:=y-t;
z:= z+t;

z := z - vMengerZ*scale2;
z := - abs(z);
z := z + vMengerZ*scale2;


  x := scale *x-vMengerX*scale1; 
  y := scale *y-vMengerY*scale1; 
  z := scale *z;

I just put the Domo variable in right place and it streched central hole into the rectangle. Moreso it was quite a lucky find as it works like an additional mirror. What is good if you use Mutagen and your intention is technological.

Maybe this is like MandeleX or MandalaY linear pull? I hadn't looked closely on that formula.

Unit vector substraction. Unit Vector = x,y,z / |x,y,z|

Code:

radius := sqrt(x*x+y*y+z*z) ;

x:= x - Thickness * x/radius ;
y:= y - Thickness * y/radius ;
z:= z - Thickness * z/radius ;

This transformation works like adding air in the balloon. Unlike sacleing larger values alsou rounds and kind of bloats the fractal according to it's shape, and negatives does the opposite.

Code:

[END]
Formula version 1.1
 
House creator based on folds and Menger Cube
(Luca GN formula MengerSmt code).

* * *
By Edgar Malinovsky

All together looks like houses. This have very chaotic behaviour. Folds influence Menger, hence if FoldZ=1 Menger 1,1,-1 will generate tower made of snowflakes. Then adding FoldY=0.2 turns outline of loose snowflakes into solid cubes and generates something like house with balconies.
This is not so good when you want to generate the house you want. Hence Mutagen is recomended.

(http://www.fractalforums.com/index.php?action=dlattach;topic=25795.0;attach=14618;image)
(http://www.fractalforums.com/index.php?action=dlattach;topic=25795.0;attach=14620;image)
(http://www.fractalforums.com/index.php?action=dlattach;topic=25795.0;attach=14621;image)

One of these formulas:
http://www.fractalforums.com/mandelbulb-3d/em-formulas-for-mandelbulb3d/

In attachment basic units modified menger. The more beautiful one is snowflake with mirrors.

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Fractal Math, Chaos Theory & Research => Sierpinski Gasket => Topic started by: Alef on June 27, 2017, 01:29:30 PM