[examples] Added: shaders_mandelbrot_set (#5282)

* [examples] Added: `shaders_mandelbrot_set`

* Simplified shader code and added comments

* Comments starting with a capital letter, and some minor fixes to adhere to the convention

examples/shaders/resources/shaders/glsl100/mandelbrot_set.fs

@@ -0,0 +1,61 @@
+#version 100
+
+#define PI 3.1415926535897932384626433832795
+
+precision highp float;
+
+// Input vertex attributes (from vertex shader)
+varying vec2 fragTexCoord;
+varying vec4 fragColor;
+
+uniform vec2 offset;            // Offset of the scale
+uniform float zoom;             // Zoom of the scale
+// NOTE: Maximum number of shader for-loop iterations depend on GPU,
+// For example, on RasperryPi for this examply only supports up to 60
+uniform int maxIterations;      // Max iterations per pixel
+
+const float max = 4.0;          // We consider infinite as 4.0: if a point reaches a distance of 4.0 it will escape to infinity
+const float max2 = max*max;     // Square of max to avoid computing square root
+
+void main()
+{
+    // The pixel coordinates are scaled so they are on the mandelbrot scale
+    // NOTE: fragTexCoord already comes as normalized screen coordinates but offset must be normalized before scaling and zoom
+    vec2 c = vec2((fragTexCoord.x - 0.5)*2.5, (fragTexCoord.y - 0.5)*1.5)/zoom;
+    c.x += offset.x;
+    c.y += offset.y;
+    float a = 0.0;
+    float b = 0.0;
+
+    // The Mandelbrot set is a two-dimensional set defined in the complex plane on which the iteration of the function
+    // Fc(z) = z^2 + c on the complex numbers c from the plane does not diverge to infinity starting at z = 0
+    // Here: z = a + bi. Iterations: z -> z^2 + c = (a + bi)^2 + (c.x + c.yi) = (a^2 - b^2 + c.x) + (2ab + c.y)i
+
+    int iter = 0;
+    while (iter < maxIterations)
+    {
+        float aa = a*a;
+        float bb = b*b;
+        if (aa + bb > max2)
+            break;
+
+        float twoab = 2.0*a*b;
+        a = aa - bb + c.x;
+        b = twoab + c.y;
+
+        ++iter;
+    }
+
+    if (iter >= maxIterations)
+    {
+        gl_FragColor = vec4(0.0, 0.0, 0.0, 1.0);
+    }
+    else
+    {
+        float normR = float(iter - (iter/55)*55)/55.0;
+        float normG = float(iter - (iter/69)*69)/69.0;
+        float normB = float(iter - (iter/40)*40)/40.0;
+
+        gl_FragColor = vec4(sin(normR*PI), sin(normG*PI), sin(normB*PI), 1.0);
+    }
+}

examples/shaders/resources/shaders/glsl120/mandelbrot_set.fs

@@ -0,0 +1,59 @@
+#version 120
+
+#define PI 3.1415926535897932384626433832795
+
+// Input vertex attributes (from vertex shader)
+varying vec2 fragTexCoord;
+varying vec4 fragColor;
+
+uniform vec2 offset;            // Offset of the scale
+uniform float zoom;             // Zoom of the scale
+// NOTE: Maximum number of shader for-loop iterations depend on GPU,
+// For example, on RasperryPi for this examply only supports up to 60
+uniform int maxIterations;      // Max iterations per pixel
+
+const float max = 4.0;          // We consider infinite as 4.0: if a point reaches a distance of 4.0 it will escape to infinity
+const float max2 = max*max;     // Square of max to avoid computing square root
+
+void main()
+{
+    // The pixel coordinates are scaled so they are on the mandelbrot scale
+    // NOTE: fragTexCoord already comes as normalized screen coordinates but offset must be normalized before scaling and zoom
+    vec2 c = vec2((fragTexCoord.x - 0.5)*2.5, (fragTexCoord.y - 0.5)*1.5)/zoom;
+    c.x += offset.x;
+    c.y += offset.y;
+    float a = 0.0;
+    float b = 0.0;
+
+    // The Mandelbrot set is a two-dimensional set defined in the complex plane on which the iteration of the function
+    // Fc(z) = z^2 + c on the complex numbers c from the plane does not diverge to infinity starting at z = 0
+    // Here: z = a + bi. Iterations: z -> z^2 + c = (a + bi)^2 + (c.x + c.yi) = (a^2 - b^2 + c.x) + (2ab + c.y)i
+
+    int iter = 0;
+    while (iter < maxIterations)
+    {
+        float aa = a*a;
+        float bb = b*b;
+        if (aa + bb > max2)
+            break;
+
+        float twoab = 2.0*a*b;
+        a = aa - bb + c.x;
+        b = twoab + c.y;
+
+        ++iter;
+    }
+
+    if (iter >= maxIterations)
+    {
+        gl_FragColor = vec4(0.0, 0.0, 0.0, 1.0);
+    }
+    else
+    {
+        float normR = float(iter - (iter/55)*55)/55.0;
+        float normG = float(iter - (iter/69)*69)/69.0;
+        float normB = float(iter - (iter/40)*40)/40.0;
+
+        gl_FragColor = vec4(sin(normR*PI), sin(normG*PI), sin(normB*PI), 1.0);
+    }
+}

examples/shaders/resources/shaders/glsl330/mandelbrot_set.fs

@@ -0,0 +1,58 @@
+#version 330
+
+#define PI 3.1415926535897932384626433832795
+
+// Input vertex attributes (from vertex shader)
+in vec2 fragTexCoord;
+in vec4 fragColor;
+
+// Output fragment color
+out vec4 finalColor;
+
+uniform vec2 offset;            // Offset of the scale
+uniform float zoom;             // Zoom of the scale
+uniform int maxIterations;      // Max iterations per pixel
+
+const float max = 4.0;          // We consider infinite as 4.0: if a point reaches a distance of 4.0 it will escape to infinity
+const float max2 = max*max;     // Square of max to avoid computing square root
+
+void main()
+{
+    // The pixel coordinates are scaled so they are on the mandelbrot scale
+    // NOTE: fragTexCoord already comes as normalized screen coordinates but offset must be normalized before scaling and zoom
+    vec2 c = vec2((fragTexCoord.x - 0.5)*2.5, (fragTexCoord.y - 0.5)*1.5)/zoom;
+    c.x += offset.x;
+    c.y += offset.y;
+    float a = 0.0;
+    float b = 0.0;
+
+    // The Mandelbrot set is a two-dimensional set defined in the complex plane on which the iteration of the function
+    // Fc(z) = z^2 + c on the complex numbers c from the plane does not diverge to infinity starting at z = 0
+    // Here: z = a + bi. Iterations: z -> z^2 + c = (a + bi)^2 + (c.x + c.yi) = (a^2 - b^2 + c.x) + (2ab + c.y)i
+
+    int iter = 0;
+    for (iter = 0; iter < maxIterations; ++iter)
+    {
+        float aa = a*a;
+        float bb = b*b;
+        if (aa + bb > max2)
+            break;
+
+        float twoab = 2.0*a*b;
+        a = aa - bb + c.x;
+        b = twoab + c.y;
+    }
+
+    if (iter >= maxIterations)
+    {
+        finalColor = vec4(0.0, 0.0, 0.0, 1.0);
+    }
+    else
+    {
+        float normR = float(iter%55)/55.0;
+        float normG = float(iter%69)/69.0;
+        float normB = float(iter%40)/40.0;
+
+        finalColor = vec4(sin(normR*PI), sin(normG*PI), sin(normB*PI), 1.0);
+    }
+}