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Mgfractal: Add 3D and 4D fractals
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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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@paramat
paramat committed Dec 15, 2015
1 parent aed1076 commit c26eb87
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Showing 4 changed files with 144 additions and 58 deletions.
51 changes: 31 additions & 20 deletions builtin/settingtypes.txt
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Expand Up @@ -970,49 +970,60 @@ mgflat_np_cave2 (Mapgen flat cave2 noise parameters) noise_params 0, 12, (128, 1

[***Mapgen fractal]

# Choice of 8 4-dimensional fractals.
# 1 = "Roundy" mandelbrot set.
# 2 = "Roundy" julia set.
# 3 = "Squarry" mandelbrot set.
# 4 = "Squarry" julia set.
# 5 = "Mandy Cousin" mandelbrot set.
# 6 = "Mandy Cousin" julia set.
# 7 = "Variation" mandelbrot set.
# 8 = "Variation" julia set.
mgfractal_formula (Mapgen fractal formula) int 1 1 8
# Choice of 18 fractals from 9 formulas.
# 1 = 4D "Roundy" mandelbrot set.
# 2 = 4D "Roundy" julia set.
# 3 = 4D "Squarry" mandelbrot set.
# 4 = 4D "Squarry" julia set.
# 5 = 4D "Mandy Cousin" mandelbrot set.
# 6 = 4D "Mandy Cousin" julia set.
# 7 = 4D "Variation" mandelbrot set.
# 8 = 4D "Variation" julia set.
# 9 = 3D "Mandelbrot/Mandelbar" mandelbrot set.
# 10 = 3D "Mandelbrot/Mandelbar" julia set.
# 11 = 3D "Christmas Tree" mandelbrot set.
# 12 = 3D "Christmas Tree" julia set.
# 13 = 3D "Mandelbulb" mandelbrot set.
# 14 = 3D "Mandelbulb" julia set.
# 15 = 3D "Cosine Mandelbulb" mandelbrot set.
# 16 = 3D "Cosine Mandelbulb" julia set.
# 17 = 4D "Mandelbulb" mandelbrot set.
# 18 = 4D "Mandelbulb" julia set.
mgfractal_fractal (Mapgen fractal fractal) int 1 1 18

# Iterations of the recursive function.
# Controls scale of finest detail.
# Controls the amount of fine detail.
mgfractal_iterations (Mapgen fractal iterations) int 11

# Approximate (X,Y,Z) scale of fractal in nodes.
mgfractal_scale (Mapgen fractal scale) v3f (4096.0, 1024.0, 4096.0)

# (X,Y,Z) offset of fractal from world centre.
# (X,Y,Z) offset of fractal from world centre in units of 'scale'.
# Used to move a suitable spawn area of low land close to (0, 0).
# The default is suitable for mandelbrot sets, it needs to be edited for julia sets,
# do this by greatly reducing 'scale' and setting 'offset' initially to (0, 0, 0).
# The default is suitable for mandelbrot sets, it needs to be edited for julia sets.
# Range roughly -2 to 2. Multiply by 'scale' for offset in nodes.
mgfractal_offset (Mapgen fractal offset) v3f (1.79, 0.0, 0.0)

# W co-ordinate of the generated 3D slice of the 4D shape.
# Alters the generated 3D shape.
# W co-ordinate of the generated 3D slice of a 4D fractal.
# Determines which 3D slice of the 4D shape is generated.
# Has no effect on 3D fractals.
# Range roughly -2 to 2.
mgfractal_slice_w (Mapgen fractal slice w) float 0.0

# Julia set only: X value determining the 4D shape.
# Julia set only: X component of hypercomplex constant determining julia shape.
# Range roughly -2 to 2.
mgfractal_julia_x (Mapgen fractal julia x) float 0.33

# Julia set only: Y value determining the 4D shape.
# Julia set only: Y component of hypercomplex constant determining julia shape.
# Range roughly -2 to 2.
mgfractal_julia_y (Mapgen fractal julia y) float 0.33

# Julia set only: Z value determining the 4D shape.
# Julia set only: Z component of hypercomplex constant determining julia shape.
# Range roughly -2 to 2.
mgfractal_julia_z (Mapgen fractal julia z) float 0.33

# Julia set only: W value determining the 4D shape.
# Julia set only: W component of hypercomplex constant determining julia shape.
# Has no effect on 3D fractals.
# Range roughly -2 to 2.
mgfractal_julia_w (Mapgen fractal julia w) float 0.33

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53 changes: 32 additions & 21 deletions minetest.conf.example
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Expand Up @@ -1234,57 +1234,68 @@

#### Mapgen fractal

# Choice of 8 4-dimensional fractals.
# 1 = "Roundy" mandelbrot set.
# 2 = "Roundy" julia set.
# 3 = "Squarry" mandelbrot set.
# 4 = "Squarry" julia set.
# 5 = "Mandy Cousin" mandelbrot set.
# 6 = "Mandy Cousin" julia set.
# 7 = "Variation" mandelbrot set.
# 8 = "Variation" julia set.
# type: int min: 1 max: 8
# mgfractal_formula = 1
# Choice of 18 fractals from 9 formulas.
# 1 = 4D "Roundy" mandelbrot set.
# 2 = 4D "Roundy" julia set.
# 3 = 4D "Squarry" mandelbrot set.
# 4 = 4D "Squarry" julia set.
# 5 = 4D "Mandy Cousin" mandelbrot set.
# 6 = 4D "Mandy Cousin" julia set.
# 7 = 4D "Variation" mandelbrot set.
# 8 = 4D "Variation" julia set.
# 9 = 3D "Mandelbrot/Mandelbar" mandelbrot set.
# 10 = 3D "Mandelbrot/Mandelbar" julia set.
# 11 = 3D "Christmas Tree" mandelbrot set.
# 12 = 3D "Christmas Tree" julia set.
# 13 = 3D "Mandelbulb" mandelbrot set.
# 14 = 3D "Mandelbulb" julia set.
# 15 = 3D "Cosine Mandelbulb" mandelbrot set.
# 16 = 3D "Cosine Mandelbulb" julia set.
# 17 = 4D "Mandelbulb" mandelbrot set.
# 18 = 4D "Mandelbulb" julia set.
# type: int min: 1 max: 18
# mgfractal_fractal = 1

# Iterations of the recursive function.
# Controls scale of finest detail.
# Controls the amount of fine detail.
# type: int
# mgfractal_iterations = 11

# Approximate (X,Y,Z) scale of fractal in nodes.
# type: v3f
# mgfractal_scale = (4096.0, 1024.0, 4096.0)

# (X,Y,Z) offset of fractal from world centre.
# (X,Y,Z) offset of fractal from world centre in units of 'scale'.
# Used to move a suitable spawn area of low land close to (0, 0).
# The default is suitable for mandelbrot sets, it needs to be edited for julia sets,
# do this by greatly reducing 'scale' and setting 'offset' initially to (0, 0, 0).
# The default is suitable for mandelbrot sets, it needs to be edited for julia sets.
# Range roughly -2 to 2. Multiply by 'scale' for offset in nodes.
# type: v3f
# mgfractal_offset = (1.79, 0.0, 0.0)

# W co-ordinate of the generated 3D slice of the 4D shape.
# Alters the generated 3D shape.
# W co-ordinate of the generated 3D slice of a 4D fractal.
# Determines which 3D slice of the 4D shape is generated.
# Has no effect on 3D fractals.
# Range roughly -2 to 2.
# type: float
# mgfractal_slice_w = 0.0

# Julia set only: X value determining the 4D shape.
# Julia set only: X component of hypercomplex constant determining julia shape.
# Range roughly -2 to 2.
# type: float
# mgfractal_julia_x = 0.33

# Julia set only: Y value determining the 4D shape.
# Julia set only: Y component of hypercomplex constant determining julia shape.
# Range roughly -2 to 2.
# type: float
# mgfractal_julia_y = 0.33

# Julia set only: Z value determining the 4D shape.
# Julia set only: Z component of hypercomplex constant determining julia shape.
# Range roughly -2 to 2.
# type: float
# mgfractal_julia_z = 0.33

# Julia set only: W value determining the 4D shape.
# Julia set only: W component of hypercomplex constant determining julia shape.
# Has no effect on 3D fractals.
# Range roughly -2 to 2.
# type: float
# mgfractal_julia_w = 0.33
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86 changes: 72 additions & 14 deletions src/mapgen_fractal.cpp
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Expand Up @@ -66,7 +66,7 @@ MapgenFractal::MapgenFractal(int mapgenid, MapgenParams *params, EmergeManager *
MapgenFractalParams *sp = (MapgenFractalParams *)params->sparams;
this->spflags = sp->spflags;

this->formula = sp->formula;
this->fractal = sp->fractal;
this->iterations = sp->iterations;
this->scale = sp->scale;
this->offset = sp->offset;
Expand All @@ -77,6 +77,9 @@ MapgenFractal::MapgenFractal(int mapgenid, MapgenParams *params, EmergeManager *
this->julia_z = sp->julia_z;
this->julia_w = sp->julia_w;

this->formula = fractal / 2 + fractal % 2;
this->julia = fractal % 2 == 0;

//// 2D terrain noise
noise_seabed = new Noise(&sp->np_seabed, seed, csize.X, csize.Z);
noise_filler_depth = new Noise(&sp->np_filler_depth, seed, csize.X, csize.Z);
Expand Down Expand Up @@ -141,7 +144,7 @@ MapgenFractalParams::MapgenFractalParams()
{
spflags = 0;

formula = 1;
fractal = 1;
iterations = 11;
scale = v3f(4096.0, 1024.0, 4096.0);
offset = v3f(1.79, 0.0, 0.0);
Expand All @@ -163,7 +166,7 @@ void MapgenFractalParams::readParams(const Settings *settings)
{
settings->getFlagStrNoEx("mgfractal_spflags", spflags, flagdesc_mapgen_fractal);

settings->getU16NoEx("mgfractal_formula", formula);
settings->getU16NoEx("mgfractal_fractal", fractal);
settings->getU16NoEx("mgfractal_iterations", iterations);
settings->getV3FNoEx("mgfractal_scale", scale);
settings->getV3FNoEx("mgfractal_offset", offset);
Expand All @@ -185,7 +188,7 @@ void MapgenFractalParams::writeParams(Settings *settings) const
{
settings->setFlagStr("mgfractal_spflags", spflags, flagdesc_mapgen_fractal, U32_MAX);

settings->setU16("mgfractal_formula", formula);
settings->setU16("mgfractal_fractal", fractal);
settings->setU16("mgfractal_iterations", iterations);
settings->setV3F("mgfractal_scale", scale);
settings->setV3F("mgfractal_offset", offset);
Expand Down Expand Up @@ -368,7 +371,7 @@ bool MapgenFractal::getFractalAtPoint(s16 x, s16 y, s16 z)
{
float cx, cy, cz, cw, ox, oy, oz, ow;

if (formula % 2 == 0) { // Julia sets, formula = 2, 4, 6, 8
if (julia) { // Julia set
cx = julia_x;
cy = julia_y;
cz = julia_z;
Expand All @@ -377,7 +380,7 @@ bool MapgenFractal::getFractalAtPoint(s16 x, s16 y, s16 z)
oy = (float)y / scale.Y - offset.Y;
oz = (float)z / scale.Z - offset.Z;
ow = slice_w;
} else { // Mandelbrot sets, formula = 1, 3, 5, 7
} else { // Mandelbrot set
cx = (float)x / scale.X - offset.X;
cy = (float)y / scale.Y - offset.Y;
cz = (float)z / scale.Z - offset.Z;
Expand All @@ -388,32 +391,87 @@ bool MapgenFractal::getFractalAtPoint(s16 x, s16 y, s16 z)
ow = 0.0f;
}

float nx = 0.0f;
float ny = 0.0f;
float nz = 0.0f;
float nw = 0.0f;

for (u16 iter = 0; iter < iterations; iter++) {
float nx = 0.0f;
float ny = 0.0f;
float nz = 0.0f;
float nw = 0.0f;

if (formula == 1 || formula == 2) { // 4D "Roundy" Mandelbrot/Julia Set
if (formula == 1) { // 4D "Roundy"
nx = ox * ox - oy * oy - oz * oz - ow * ow + cx;
ny = 2.0f * (ox * oy + oz * ow) + cy;
nz = 2.0f * (ox * oz + oy * ow) + cz;
nw = 2.0f * (ox * ow + oy * oz) + cw;
} else if (formula == 3 || formula == 4) { // 4D "Squarry" Mandelbrot/Julia Set
} else if (formula == 2) { // 4D "Squarry"
nx = ox * ox - oy * oy - oz * oz - ow * ow + cx;
ny = 2.0f * (ox * oy + oz * ow) + cy;
nz = 2.0f * (ox * oz + oy * ow) + cz;
nw = 2.0f * (ox * ow - oy * oz) + cw;
} else if (formula == 5 || formula == 6) { // 4D "Mandy Cousin" Mandelbrot/Julia Set
} else if (formula == 3) { // 4D "Mandy Cousin"
nx = ox * ox - oy * oy - oz * oz + ow * ow + cx;
ny = 2.0f * (ox * oy + oz * ow) + cy;
nz = 2.0f * (ox * oz + oy * ow) + cz;
nw = 2.0f * (ox * ow + oy * oz) + cw;
} else if (formula == 7 || formula == 8) { // 4D "Variation" Mandelbrot/Julia Set
} else if (formula == 4) { // 4D "Variation"
nx = ox * ox - oy * oy - oz * oz - ow * ow + cx;
ny = 2.0f * (ox * oy + oz * ow) + cy;
nz = 2.0f * (ox * oz - oy * ow) + cz;
nw = 2.0f * (ox * ow + oy * oz) + cw;
} else if (formula == 5) { // 3D "Mandelbrot/Mandelbar"
nx = ox * ox - oy * oy - oz * oz + cx;
ny = 2.0f * ox * oy + cy;
nz = -2.0f * ox * oz + cz;
} else if (formula == 6) { // 3D "Christmas Tree"
// Altering the formula here is necessary to avoid division by zero
if (fabs(oz) < 0.000000001f) {
nx = ox * ox - oy * oy - oz * oz + cx;
ny = 2.0f * oy * ox + cy;
nz = 4.0f * oz * ox + cz;
} else {
float a = (2.0f * ox) / (sqrt(oy * oy + oz * oz));
nx = ox * ox - oy * oy - oz * oz + cx;
ny = a * (oy * oy - oz * oz) + cy;
nz = a * 2.0f * oy * oz + cz;
}
} else if (formula == 7) { // 3D "Mandelbulb"
if (fabs(oy) < 0.000000001f) {
nx = ox * ox - oz * oz + cx;
ny = cy;
nz = -2.0f * oz * sqrt(ox * ox) + cz;
} else {
float a = 1.0f - (oz * oz) / (ox * ox + oy * oy);
nx = (ox * ox - oy * oy) * a + cx;
ny = 2.0f * ox * oy * a + cy;
nz = -2.0f * oz * sqrt(ox * ox + oy * oy) + cz;
}
} else if (formula == 8) { // 3D "Cosine Mandelbulb"
if (fabs(oy) < 0.000000001f) {
nx = 2.0f * ox * oz + cx;
ny = 4.0f * oy * oz + cy;
nz = oz * oz - ox * ox - oy * oy + cz;
} else {
float a = (2.0f * oz) / sqrt(ox * ox + oy * oy);
nx = (ox * ox - oy * oy) * a + cx;
ny = 2.0f * ox * oy * a + cy;
nz = oz * oz - ox * ox - oy * oy + cz;
}
} else if (formula == 9) { // 4D "Mandelbulb"
float rxy = sqrt(ox * ox + oy * oy);
float rxyz = sqrt(ox * ox + oy * oy + oz * oz);
if (fabs(ow) < 0.000000001f && fabs(oz) < 0.000000001f) {
nx = (ox * ox - oy * oy) + cx;
ny = 2.0f * ox * oy + cy;
nz = -2.0f * rxy * oz + cz;
nw = 2.0f * rxyz * ow + cw;
} else {
float a = 1.0f - (ow * ow) / (rxyz * rxyz);
float b = a * (1.0f - (oz * oz) / (rxy * rxy));
nx = (ox * ox - oy * oy) * b + cx;
ny = 2.0f * ox * oy * b + cy;
nz = -2.0f * rxy * oz * a + cz;
nw = 2.0f * rxyz * ow + cw;
}
}

if (nx * nx + ny * ny + nz * nz + nw * nw > 4.0f)
Expand Down
12 changes: 9 additions & 3 deletions src/mapgen_fractal.h
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Expand Up @@ -3,6 +3,9 @@ Minetest
Copyright (C) 2010-2015 kwolekr, Ryan Kwolek <kwolekr@minetest.net>
Copyright (C) 2010-2015 paramat, Matt Gregory
Fractal formulas from http://www.bugman123.com/Hypercomplex/index.html
by Paul Nylander, and from http://www.fractalforums.com, thank you.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or
Expand Down Expand Up @@ -33,7 +36,7 @@ extern FlagDesc flagdesc_mapgen_fractal[];
struct MapgenFractalParams : public MapgenSpecificParams {
u32 spflags;

u16 formula;
u16 fractal;
u16 iterations;
v3f scale;
v3f offset;
Expand Down Expand Up @@ -63,14 +66,17 @@ class MapgenFractal : public Mapgen {

int ystride;
int zstride;
u32 spflags;
u16 formula;
bool julia;

v3s16 node_min;
v3s16 node_max;
v3s16 full_node_min;
v3s16 full_node_max;

u16 formula;
u32 spflags;

u16 fractal;
u16 iterations;
v3f scale;
v3f offset;
Expand Down

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