OpenGL fractal Sierpinski trim pad

Sierpinski triangle:

Sierpinski cushion:

It is a very interesting pattern with a long history. It has aroused great interest in the field of fractal ry. It is a geometric shape defined by recursion and random, in extreme conditions, its properties are not random:

Generation Method:

Generate Sierpinski fill padAlgorithmDescription:

(1) randomly select a vertex inside the triangle as the initial vertex.

(2) randomly select one of the three triangle vertices, find the midpoint between the vertex and the initial vertex, and draw the midpoint

(3) Use the midpoint in (2) as the initial point to (2)

Implementation Method (OpenGL C #):

 1   Using System; 2   Using System. Collections. Generic;  3   Using  System. LINQ;  4   Using  System. text;  5   6   Using  Tao. OpenGL;  7   Using  Tao. freeglut;  8   Using Tao. Platform. windows;  9   10   Class  Program  11   {  12       Static   String Title = "  Sierpinski Cushion  "  ;  13       ///   <Summary> 14       ///  Initialization  15       ///   </Summary>  16       Static   Void  Myinit ()  17   {  18           //  Set attributes  19 Gl. glclearcolor ( 0.0f ,0.0f , 0.0f , 1.0f ); //  Background Color  20   21           //  Create View  22   Gl. glmatrixmode (GL. gl_projection );  23   Gl. glloadidentity ();  24 Glu. gluortho2d ( 0.0 ,600.0 , 0.0 , 600.0  );  25   }  26       ///   <Summary>  27       ///  Plotting Functions  28       ///   </Summary>  29       Static  Void  Display ()  30   {  31           //  Define an arbitrary triangle on the zplane  32           Float [,] Vertices = New   Float [ 3 , 3 ] { 0.0f , 0.0f ,0.0f  },{ 300f, 600f, 0f}, {600f, 0f, 0f }};  33           34           //  Define the initial point position  35           Float [] P = New   Float [ 3 ] { 7.5f , 5.0f , 0.0f  };  36 Random rand1 = New  Random ();  37       38   Gl. glclear (GL. gl_color_buffer_bit );  39 Gl. glcolor3f ( 1.0f , 0.5f , 0.5f ); //  Color  40   41   Gl. glbegin (GL. gl_points ); 42           For ( Int K = 0 ; K < 50000 ; K ++ )  43   {  44               Int J = rand1.next () % 3  ;  45   46 P [ 0 ] = (P [0 ] + Vertices [J, 0 ])/ 2  ;  47 P [ 1 ] = (P [ 1 ] + Vertices [J, 1 ])/ 2  ;  48   49   Gl. glvertex3fv (P );  50   } 51   Gl. glend ();  52   53   Gl. glflush ();  54   }  55   56   57       Static   Void Reshape ( Int W, Int  H)  58   { 59   60   }  61   62       Static   Void Main ( String  [] ARGs)  63   {  64   GLUT. gluinit ();  65 GLUT. gluinitdisplaymode (GLUT. glu_rgba | GLUT. glu_single );  66 GLUT. gluinitwindowposition ( 400 , 100  );  67 GLUT. gluinitwindowsize ( 600 , 600  );  68   GLUT. glucreatewindow (title );  69   70           71   Myinit ();  72  GLUT. gludisplayfunc (Display );  73          //  GLUT. glureshapefunc (reshape );  74   GLUT. glumainloop ();  75   }  76 }