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-rw-r--r--builtin/settingtypes.txt51
-rw-r--r--minetest.conf.example53
-rw-r--r--src/mapgen_fractal.cpp86
-rw-r--r--src/mapgen_fractal.h12
4 files changed, 144 insertions, 58 deletions
diff --git a/builtin/settingtypes.txt b/builtin/settingtypes.txt
index 4a714e1aa..62f817062 100644
--- a/builtin/settingtypes.txt
+++ b/builtin/settingtypes.txt
@@ -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
diff --git a/minetest.conf.example b/minetest.conf.example
index 34d618fd5..40456f953 100644
--- a/minetest.conf.example
+++ b/minetest.conf.example
@@ -1234,20 +1234,30 @@
#### 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
@@ -1255,36 +1265,37 @@
# 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
diff --git a/src/mapgen_fractal.cpp b/src/mapgen_fractal.cpp
index 14dfe5c85..6c03c4ca9 100644
--- a/src/mapgen_fractal.cpp
+++ b/src/mapgen_fractal.cpp
@@ -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;
@@ -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);
@@ -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);
@@ -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);
@@ -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);
@@ -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;
@@ -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;
@@ -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)
diff --git a/src/mapgen_fractal.h b/src/mapgen_fractal.h
index 7d31a43b8..3d4f7ee8f 100644
--- a/src/mapgen_fractal.h
+++ b/src/mapgen_fractal.h
@@ -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
@@ -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;
@@ -63,14 +66,17 @@ public:
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;
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-03 02:29:36 +0000