Add more fractals and decompose slightly

Author: 3b1b

manimlib/shaders/inserts/complex_functions.glsl

@@ -0,0 +1,15 @@
+vec2 complex_mult(vec2 z, vec2 w){
+    return vec2(z.x * w.x - z.y * w.y, z.x * w.y + z.y * w.x);
+}
+
+vec2 complex_div(vec2 z, vec2 w){
+    return complex_mult(z, vec2(w.x, -w.y)) / (w.x * w.x + w.y * w.y);
+}
+
+vec2 complex_pow(vec2 z, int n){
+    vec2 result = vec2(1.0, 0.0);
+    for(int i = 0; i < n; i++){
+        result = complex_mult(result, z);
+    }
+    return result;
+}

manimlib/shaders/mandelbrot_fractal/frag.glsl

@@ -0,0 +1,77 @@
+#version 330
+
+uniform vec3 light_source_position;
+uniform float gloss;
+uniform float shadow;
+uniform float focal_distance;
+
+uniform vec2 parameter;
+uniform float opacity;
+uniform float n_steps;
+uniform float mandelbrot;
+
+uniform vec3 color0;
+uniform vec3 color1;
+uniform vec3 color2;
+uniform vec3 color3;
+uniform vec3 color4;
+uniform vec3 color5;
+uniform vec3 color6;
+uniform vec3 color7;
+uniform vec3 color8;
+
+uniform vec2 frame_shape;
+
+in vec3 xyz_coords;
+
+out vec4 frag_color;
+
+#INSERT finalize_color.glsl
+#INSERT complex_functions.glsl
+
+const int MAX_DEGREE = 5;
+
+void main() {
+    vec3 color_map[9] = vec3[9](
+        color0, color1, color2, color3,
+        color4, color5, color6, color7, color8
+    );
+    vec3 color;
+
+    vec2 z;
+    vec2 c;
+
+    if(bool(mandelbrot)){
+        c = xyz_coords.xy;
+        z = vec2(0.0, 0.0);
+    }else{
+        c = parameter;
+        z = xyz_coords.xy;
+    }
+
+    float outer_bound = 2.0;
+    bool stable = true;
+    for(int n = 0; n < int(n_steps); n++){
+        z = complex_mult(z, z) + c;
+        if(length(z) > outer_bound){
+            float float_n = float(n);
+            float_n += log(outer_bound) / log(length(z));
+            float_n += 0.5 * length(c);
+            color = float_to_color(sqrt(float_n), 1.5, 8.0, color_map);
+            stable = false;
+            break;
+        }
+    }
+    if(stable){
+        color = vec3(0.0, 0.0, 0.0);
+    }
+
+    frag_color = finalize_color(
+        vec4(color, opacity),
+        xyz_coords,
+        vec3(0.0, 0.0, 1.0),
+        light_source_position,
+        gloss,
+        shadow
+    );
+ }

manimlib/shaders/mandelbrot_fractal/vert.glsl

@@ -0,0 +1,17 @@
+#version 330
+
+#INSERT camera_uniform_declarations.glsl
+
+in vec3 point;
+out vec3 xyz_coords;
+
+uniform float scale_factor;
+uniform vec3 offset;
+
+#INSERT position_point_into_frame.glsl
+#INSERT get_gl_Position.glsl
+
+void main(){
+    xyz_coords = (point - offset) / scale_factor;
+    gl_Position = get_gl_Position(position_point_into_frame(point));
+}

manimlib/shaders/meta_poly_fractal/frag.glsl

@@ -31,25 +31,10 @@ in vec3 xyz_coords;
 out vec4 frag_color;
 
 #INSERT finalize_color.glsl
+#INSERT complex_functions.glsl
 
 const int MAX_DEGREE = 3;
 
-vec2 complex_mult(vec2 z, vec2 w){
-    return vec2(z.x * w.x - z.y * w.y, z.x * w.y + z.y * w.x);
-}
-
-vec2 complex_div(vec2 z, vec2 w){
-    return complex_mult(z, vec2(w.x, -w.y)) / (w.x * w.x + w.y * w.y);
-}
-
-vec2 complex_pow(vec2 z, int n){
-    vec2 result = vec2(1.0, 0.0);
-    for(int i = 0; i < n; i++){
-        result = complex_mult(result, z);
-    }
-    return result;
-}
-
 vec2 poly(vec2 z, vec2[MAX_DEGREE + 1] coefs){
     vec2 result = vec2(0.0);
     for(int n = 0; n < int(n_roots) + 1; n++){

manimlib/shaders/poly_fractal/frag.glsl

@@ -28,6 +28,7 @@ uniform float n_roots;
 uniform float n_steps;
 uniform float julia_highlight;
 uniform float color_mult;
+uniform float black_for_cycles;
 
 uniform vec2 frame_shape;
 
@@ -36,24 +37,10 @@ in vec3 xyz_coords;
 out vec4 frag_color;
 
 #INSERT finalize_color.glsl
+#INSERT complex_functions.glsl
 
 const int MAX_DEGREE = 5;
 
-vec2 complex_mult(vec2 z, vec2 w){
-    return vec2(z.x * w.x - z.y * w.y, z.x * w.y + z.y * w.x);
-}
-
-vec2 complex_div(vec2 z, vec2 w){
-    return complex_mult(z, vec2(w.x, -w.y)) / (w.x * w.x + w.y * w.y);
-}
-
-vec2 complex_pow(vec2 z, int n){
-    vec2 result = vec2(1.0, 0.0);
-    for(int i = 0; i < n; i++){
-        result = complex_mult(result, z);
-    }
-    return result;
-}
 
 vec2 poly(vec2 z, vec2[MAX_DEGREE + 1] coefs){
     vec2 result = vec2(0.0);
@@ -113,6 +100,10 @@ void main() {
     }
     color *= (1.0 + (color_mult - 1) * (n_iters - 5));
 
+    if(black_for_cycles > 0.0 && min_dist > 1e-2){
+        color = vec4(0.0, 0.0, 0.0, 1.0);
+    }
+
     // if(julia_highlight > 0.0){
     //     float factor = min_dist / distance(z, found_root);
     //     factor *= pow(2.0, n_iters);