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Mgfractal: Add 3D and 4D fractals
3D Mandelbrot/Mandelbar 3D Christmas Tree 3D Mandelbulb 3D Cosine Mandelbulb 4D Mandelbulb Plus corresponding julia set for each Add credits for formulas Rename parameter 'formula' to 'fractal' Speed optimisations
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@ -970,49 +970,60 @@ mgflat_np_cave2 (Mapgen flat cave2 noise parameters) noise_params 0, 12, (128, 1
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[***Mapgen fractal]
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# Choice of 8 4-dimensional fractals.
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# 1 = "Roundy" mandelbrot set.
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# 2 = "Roundy" julia set.
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# 3 = "Squarry" mandelbrot set.
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# 4 = "Squarry" julia set.
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# 5 = "Mandy Cousin" mandelbrot set.
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# 6 = "Mandy Cousin" julia set.
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# 7 = "Variation" mandelbrot set.
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# 8 = "Variation" julia set.
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mgfractal_formula (Mapgen fractal formula) int 1 1 8
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# Choice of 18 fractals from 9 formulas.
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# 1 = 4D "Roundy" mandelbrot set.
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# 2 = 4D "Roundy" julia set.
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# 3 = 4D "Squarry" mandelbrot set.
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# 4 = 4D "Squarry" julia set.
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# 5 = 4D "Mandy Cousin" mandelbrot set.
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# 6 = 4D "Mandy Cousin" julia set.
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# 7 = 4D "Variation" mandelbrot set.
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# 8 = 4D "Variation" julia set.
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# 9 = 3D "Mandelbrot/Mandelbar" mandelbrot set.
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# 10 = 3D "Mandelbrot/Mandelbar" julia set.
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# 11 = 3D "Christmas Tree" mandelbrot set.
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# 12 = 3D "Christmas Tree" julia set.
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# 13 = 3D "Mandelbulb" mandelbrot set.
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# 14 = 3D "Mandelbulb" julia set.
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# 15 = 3D "Cosine Mandelbulb" mandelbrot set.
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# 16 = 3D "Cosine Mandelbulb" julia set.
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# 17 = 4D "Mandelbulb" mandelbrot set.
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# 18 = 4D "Mandelbulb" julia set.
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mgfractal_fractal (Mapgen fractal fractal) int 1 1 18
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# Iterations of the recursive function.
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# Controls scale of finest detail.
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# Controls the amount of fine detail.
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mgfractal_iterations (Mapgen fractal iterations) int 11
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# Approximate (X,Y,Z) scale of fractal in nodes.
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mgfractal_scale (Mapgen fractal scale) v3f (4096.0, 1024.0, 4096.0)
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# (X,Y,Z) offset of fractal from world centre.
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# (X,Y,Z) offset of fractal from world centre in units of 'scale'.
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# Used to move a suitable spawn area of low land close to (0, 0).
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# The default is suitable for mandelbrot sets, it needs to be edited for julia sets,
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# do this by greatly reducing 'scale' and setting 'offset' initially to (0, 0, 0).
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# The default is suitable for mandelbrot sets, it needs to be edited for julia sets.
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# Range roughly -2 to 2. Multiply by 'scale' for offset in nodes.
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mgfractal_offset (Mapgen fractal offset) v3f (1.79, 0.0, 0.0)
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# W co-ordinate of the generated 3D slice of the 4D shape.
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# Alters the generated 3D shape.
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# W co-ordinate of the generated 3D slice of a 4D fractal.
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# Determines which 3D slice of the 4D shape is generated.
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# Has no effect on 3D fractals.
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# Range roughly -2 to 2.
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mgfractal_slice_w (Mapgen fractal slice w) float 0.0
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# Julia set only: X value determining the 4D shape.
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# Julia set only: X component of hypercomplex constant determining julia shape.
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# Range roughly -2 to 2.
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mgfractal_julia_x (Mapgen fractal julia x) float 0.33
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# Julia set only: Y value determining the 4D shape.
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# Julia set only: Y component of hypercomplex constant determining julia shape.
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# Range roughly -2 to 2.
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mgfractal_julia_y (Mapgen fractal julia y) float 0.33
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# Julia set only: Z value determining the 4D shape.
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# Julia set only: Z component of hypercomplex constant determining julia shape.
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# Range roughly -2 to 2.
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mgfractal_julia_z (Mapgen fractal julia z) float 0.33
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# Julia set only: W value determining the 4D shape.
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# Julia set only: W component of hypercomplex constant determining julia shape.
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# Has no effect on 3D fractals.
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# Range roughly -2 to 2.
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mgfractal_julia_w (Mapgen fractal julia w) float 0.33
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@ -1234,20 +1234,30 @@
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#### Mapgen fractal
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# Choice of 8 4-dimensional fractals.
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# 1 = "Roundy" mandelbrot set.
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# 2 = "Roundy" julia set.
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# 3 = "Squarry" mandelbrot set.
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# 4 = "Squarry" julia set.
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# 5 = "Mandy Cousin" mandelbrot set.
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# 6 = "Mandy Cousin" julia set.
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# 7 = "Variation" mandelbrot set.
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# 8 = "Variation" julia set.
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# type: int min: 1 max: 8
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# mgfractal_formula = 1
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# Choice of 18 fractals from 9 formulas.
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# 1 = 4D "Roundy" mandelbrot set.
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# 2 = 4D "Roundy" julia set.
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# 3 = 4D "Squarry" mandelbrot set.
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# 4 = 4D "Squarry" julia set.
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# 5 = 4D "Mandy Cousin" mandelbrot set.
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# 6 = 4D "Mandy Cousin" julia set.
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# 7 = 4D "Variation" mandelbrot set.
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# 8 = 4D "Variation" julia set.
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# 9 = 3D "Mandelbrot/Mandelbar" mandelbrot set.
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# 10 = 3D "Mandelbrot/Mandelbar" julia set.
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# 11 = 3D "Christmas Tree" mandelbrot set.
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# 12 = 3D "Christmas Tree" julia set.
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# 13 = 3D "Mandelbulb" mandelbrot set.
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# 14 = 3D "Mandelbulb" julia set.
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# 15 = 3D "Cosine Mandelbulb" mandelbrot set.
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# 16 = 3D "Cosine Mandelbulb" julia set.
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# 17 = 4D "Mandelbulb" mandelbrot set.
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# 18 = 4D "Mandelbulb" julia set.
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# type: int min: 1 max: 18
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# mgfractal_fractal = 1
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# Iterations of the recursive function.
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# Controls scale of finest detail.
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# Controls the amount of fine detail.
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# type: int
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# mgfractal_iterations = 11
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@ -1255,36 +1265,37 @@
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# type: v3f
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# mgfractal_scale = (4096.0, 1024.0, 4096.0)
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# (X,Y,Z) offset of fractal from world centre.
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# (X,Y,Z) offset of fractal from world centre in units of 'scale'.
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# Used to move a suitable spawn area of low land close to (0, 0).
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# The default is suitable for mandelbrot sets, it needs to be edited for julia sets,
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# do this by greatly reducing 'scale' and setting 'offset' initially to (0, 0, 0).
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# The default is suitable for mandelbrot sets, it needs to be edited for julia sets.
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# Range roughly -2 to 2. Multiply by 'scale' for offset in nodes.
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# type: v3f
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# mgfractal_offset = (1.79, 0.0, 0.0)
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# W co-ordinate of the generated 3D slice of the 4D shape.
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# Alters the generated 3D shape.
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# W co-ordinate of the generated 3D slice of a 4D fractal.
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# Determines which 3D slice of the 4D shape is generated.
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# Has no effect on 3D fractals.
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# Range roughly -2 to 2.
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# type: float
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# mgfractal_slice_w = 0.0
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# Julia set only: X value determining the 4D shape.
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# Julia set only: X component of hypercomplex constant determining julia shape.
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# Range roughly -2 to 2.
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# type: float
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# mgfractal_julia_x = 0.33
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# Julia set only: Y value determining the 4D shape.
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# Julia set only: Y component of hypercomplex constant determining julia shape.
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# Range roughly -2 to 2.
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# type: float
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# mgfractal_julia_y = 0.33
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# Julia set only: Z value determining the 4D shape.
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# Julia set only: Z component of hypercomplex constant determining julia shape.
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# Range roughly -2 to 2.
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# type: float
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# mgfractal_julia_z = 0.33
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# Julia set only: W value determining the 4D shape.
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# Julia set only: W component of hypercomplex constant determining julia shape.
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# Has no effect on 3D fractals.
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# Range roughly -2 to 2.
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# type: float
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# mgfractal_julia_w = 0.33
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@ -66,7 +66,7 @@ MapgenFractal::MapgenFractal(int mapgenid, MapgenParams *params, EmergeManager *
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MapgenFractalParams *sp = (MapgenFractalParams *)params->sparams;
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this->spflags = sp->spflags;
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this->formula = sp->formula;
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this->fractal = sp->fractal;
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this->iterations = sp->iterations;
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this->scale = sp->scale;
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this->offset = sp->offset;
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@ -77,6 +77,9 @@ MapgenFractal::MapgenFractal(int mapgenid, MapgenParams *params, EmergeManager *
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this->julia_z = sp->julia_z;
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this->julia_w = sp->julia_w;
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this->formula = fractal / 2 + fractal % 2;
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this->julia = fractal % 2 == 0;
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//// 2D terrain noise
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noise_seabed = new Noise(&sp->np_seabed, seed, csize.X, csize.Z);
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noise_filler_depth = new Noise(&sp->np_filler_depth, seed, csize.X, csize.Z);
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@ -141,7 +144,7 @@ MapgenFractalParams::MapgenFractalParams()
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{
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spflags = 0;
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formula = 1;
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fractal = 1;
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iterations = 11;
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scale = v3f(4096.0, 1024.0, 4096.0);
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offset = v3f(1.79, 0.0, 0.0);
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@ -163,7 +166,7 @@ void MapgenFractalParams::readParams(const Settings *settings)
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{
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settings->getFlagStrNoEx("mgfractal_spflags", spflags, flagdesc_mapgen_fractal);
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settings->getU16NoEx("mgfractal_formula", formula);
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settings->getU16NoEx("mgfractal_fractal", fractal);
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settings->getU16NoEx("mgfractal_iterations", iterations);
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settings->getV3FNoEx("mgfractal_scale", scale);
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settings->getV3FNoEx("mgfractal_offset", offset);
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@ -185,7 +188,7 @@ void MapgenFractalParams::writeParams(Settings *settings) const
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{
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settings->setFlagStr("mgfractal_spflags", spflags, flagdesc_mapgen_fractal, U32_MAX);
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settings->setU16("mgfractal_formula", formula);
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settings->setU16("mgfractal_fractal", fractal);
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settings->setU16("mgfractal_iterations", iterations);
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settings->setV3F("mgfractal_scale", scale);
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settings->setV3F("mgfractal_offset", offset);
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@ -368,7 +371,7 @@ bool MapgenFractal::getFractalAtPoint(s16 x, s16 y, s16 z)
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{
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float cx, cy, cz, cw, ox, oy, oz, ow;
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if (formula % 2 == 0) { // Julia sets, formula = 2, 4, 6, 8
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if (julia) { // Julia set
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cx = julia_x;
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cy = julia_y;
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cz = julia_z;
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@ -377,7 +380,7 @@ bool MapgenFractal::getFractalAtPoint(s16 x, s16 y, s16 z)
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oy = (float)y / scale.Y - offset.Y;
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oz = (float)z / scale.Z - offset.Z;
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ow = slice_w;
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} else { // Mandelbrot sets, formula = 1, 3, 5, 7
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} else { // Mandelbrot set
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cx = (float)x / scale.X - offset.X;
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cy = (float)y / scale.Y - offset.Y;
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cz = (float)z / scale.Z - offset.Z;
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@ -388,32 +391,87 @@ bool MapgenFractal::getFractalAtPoint(s16 x, s16 y, s16 z)
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ow = 0.0f;
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}
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for (u16 iter = 0; iter < iterations; iter++) {
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float nx = 0.0f;
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float ny = 0.0f;
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float nz = 0.0f;
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float nw = 0.0f;
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if (formula == 1 || formula == 2) { // 4D "Roundy" Mandelbrot/Julia Set
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for (u16 iter = 0; iter < iterations; iter++) {
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if (formula == 1) { // 4D "Roundy"
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nx = ox * ox - oy * oy - oz * oz - ow * ow + cx;
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ny = 2.0f * (ox * oy + oz * ow) + cy;
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nz = 2.0f * (ox * oz + oy * ow) + cz;
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nw = 2.0f * (ox * ow + oy * oz) + cw;
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} else if (formula == 3 || formula == 4) { // 4D "Squarry" Mandelbrot/Julia Set
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} else if (formula == 2) { // 4D "Squarry"
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nx = ox * ox - oy * oy - oz * oz - ow * ow + cx;
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ny = 2.0f * (ox * oy + oz * ow) + cy;
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nz = 2.0f * (ox * oz + oy * ow) + cz;
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nw = 2.0f * (ox * ow - oy * oz) + cw;
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} else if (formula == 5 || formula == 6) { // 4D "Mandy Cousin" Mandelbrot/Julia Set
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} else if (formula == 3) { // 4D "Mandy Cousin"
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nx = ox * ox - oy * oy - oz * oz + ow * ow + cx;
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ny = 2.0f * (ox * oy + oz * ow) + cy;
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nz = 2.0f * (ox * oz + oy * ow) + cz;
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nw = 2.0f * (ox * ow + oy * oz) + cw;
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} else if (formula == 7 || formula == 8) { // 4D "Variation" Mandelbrot/Julia Set
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} else if (formula == 4) { // 4D "Variation"
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nx = ox * ox - oy * oy - oz * oz - ow * ow + cx;
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ny = 2.0f * (ox * oy + oz * ow) + cy;
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nz = 2.0f * (ox * oz - oy * ow) + cz;
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nw = 2.0f * (ox * ow + oy * oz) + cw;
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} else if (formula == 5) { // 3D "Mandelbrot/Mandelbar"
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nx = ox * ox - oy * oy - oz * oz + cx;
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ny = 2.0f * ox * oy + cy;
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nz = -2.0f * ox * oz + cz;
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} else if (formula == 6) { // 3D "Christmas Tree"
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// Altering the formula here is necessary to avoid division by zero
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if (fabs(oz) < 0.000000001f) {
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nx = ox * ox - oy * oy - oz * oz + cx;
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ny = 2.0f * oy * ox + cy;
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nz = 4.0f * oz * ox + cz;
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} else {
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float a = (2.0f * ox) / (sqrt(oy * oy + oz * oz));
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nx = ox * ox - oy * oy - oz * oz + cx;
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ny = a * (oy * oy - oz * oz) + cy;
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nz = a * 2.0f * oy * oz + cz;
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}
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} else if (formula == 7) { // 3D "Mandelbulb"
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if (fabs(oy) < 0.000000001f) {
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nx = ox * ox - oz * oz + cx;
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ny = cy;
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nz = -2.0f * oz * sqrt(ox * ox) + cz;
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} else {
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float a = 1.0f - (oz * oz) / (ox * ox + oy * oy);
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nx = (ox * ox - oy * oy) * a + cx;
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ny = 2.0f * ox * oy * a + cy;
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nz = -2.0f * oz * sqrt(ox * ox + oy * oy) + cz;
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}
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} else if (formula == 8) { // 3D "Cosine Mandelbulb"
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if (fabs(oy) < 0.000000001f) {
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nx = 2.0f * ox * oz + cx;
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ny = 4.0f * oy * oz + cy;
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nz = oz * oz - ox * ox - oy * oy + cz;
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} else {
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float a = (2.0f * oz) / sqrt(ox * ox + oy * oy);
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nx = (ox * ox - oy * oy) * a + cx;
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ny = 2.0f * ox * oy * a + cy;
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nz = oz * oz - ox * ox - oy * oy + cz;
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}
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} else if (formula == 9) { // 4D "Mandelbulb"
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float rxy = sqrt(ox * ox + oy * oy);
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float rxyz = sqrt(ox * ox + oy * oy + oz * oz);
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if (fabs(ow) < 0.000000001f && fabs(oz) < 0.000000001f) {
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nx = (ox * ox - oy * oy) + cx;
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ny = 2.0f * ox * oy + cy;
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nz = -2.0f * rxy * oz + cz;
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nw = 2.0f * rxyz * ow + cw;
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} else {
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float a = 1.0f - (ow * ow) / (rxyz * rxyz);
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float b = a * (1.0f - (oz * oz) / (rxy * rxy));
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nx = (ox * ox - oy * oy) * b + cx;
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ny = 2.0f * ox * oy * b + cy;
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nz = -2.0f * rxy * oz * a + cz;
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nw = 2.0f * rxyz * ow + cw;
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}
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}
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if (nx * nx + ny * ny + nz * nz + nw * nw > 4.0f)
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@ -3,6 +3,9 @@ Minetest
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Copyright (C) 2010-2015 kwolekr, Ryan Kwolek <kwolekr@minetest.net>
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Copyright (C) 2010-2015 paramat, Matt Gregory
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Fractal formulas from http://www.bugman123.com/Hypercomplex/index.html
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by Paul Nylander, and from http://www.fractalforums.com, thank you.
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This program is free software; you can redistribute it and/or modify
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it under the terms of the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 2.1 of the License, or
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@ -33,7 +36,7 @@ extern FlagDesc flagdesc_mapgen_fractal[];
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struct MapgenFractalParams : public MapgenSpecificParams {
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u32 spflags;
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u16 formula;
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u16 fractal;
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u16 iterations;
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v3f scale;
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v3f offset;
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@ -63,14 +66,17 @@ public:
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int ystride;
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int zstride;
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u32 spflags;
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u16 formula;
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bool julia;
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v3s16 node_min;
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v3s16 node_max;
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v3s16 full_node_min;
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v3s16 full_node_max;
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u16 formula;
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u32 spflags;
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u16 fractal;
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u16 iterations;
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v3f scale;
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||||
v3f offset;
|
||||
|
||||
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Reference in New Issue
Block a user