We can combine the Koch snowflake fractal with the Sierpinski triangle and add some color to create a more harmonious and visually interesting fractal! Here's an example program that does just that:
' Koch Snowflake Fractal with Sierpinski Triangle and Color
' Oxygen Basic, ConsoleG, OpenGL
' frank bruebach, 12-04-2024
#compact
%filename "koch_sierpinski.exe"
'uses RTL64
% Title "Koch Snowflake Fractal with Sierpinski Triangle and Color"
'% WindowStyle WS_OVERLAPPEDWINDOW
'% Animated
'% ScaleUp
% PlaceCentral
% AnchorCentral
% shaders
uses consoleG
BeginScript
procedure drawLine(float x1, float y1, float x2, float y2, float r, float g, float b) {
color(r, g, b);
glBegin(GL_LINES);
glVertex2f(x1, y1);
glVertex2f(x2, y2);
glEnd();
}
procedure koch(float x1, float y1, float x2, float y2, int level, float r, float g, float b) {
if (level == 0) {
drawLine(x1, y1, x2, y2, r, g, b);
return;
}
float dx = x2 - x1;
float dy = y2 - y1;
float len = sqrt(dx*dx + dy*dy) / 3.0;
float angle = atan2(dy, dx);
float x3 = x1 + len * cos(angle);
float y3 = y1 + len * sin(angle);
float x4 = x3 + len * cos(angle + PI / 3.0);
float y4 = y3 + len * sin(angle + PI / 3.0);
float x5 = x2 - len * cos(angle);
float y5 = y2 - len * sin(angle);
koch(x1, y1, x3, y3, level-1, r, g, b);
koch(x3, y3, x4, y4, level-1, g, b, r);
koch(x4, y4, x5, y5, level-1, b, r, g);
koch(x5, y5, x2, y2, level-1, r, g, b);
if (level == 1) {
drawLine(x3, y3, x4, y4, g, b, r);
drawLine(x4, y4, x5, y5, b, r, g);
drawLine(x5, y5, x3, y3, r, g, b);
}
}
procedure sierpinski(float x1, float y1, float x2, float y2, float x3, float y3, int level, float r, float g, float b) {
if (level == 0) {
return;
}
float midX1 = x1 + 0.5 * (x2 - x1);
float midY1 = y1 + 0.5 * (y2 - y1);
float midX2 = x2 + 0.5 * (x3 - x2);
float midY2 = y2 + 0.5 * (y3 - y2);
float midX3 = x3 + 0.5 * (x1 - x3);
float midY3 = y3 + 0.5 * (y1 - y3);
sierpinski(x1, y1, midX1, midY1, midX3, midY3, level-1, r, g, b);
sierpinski(x2, y2, midX2, midY2, midX1, midY1, level-1, g, b, r);
sierpinski(x3, y3, midX3, midY3, midX2, midY2, level-1, b, r, g);
if (level == 1) {
drawLine(midX1, midY1, midX2, midY2, g, b, r);
drawLine(midX2, midY2, midX3, midY3, b, r, g);
drawLine(midX3, midY3, midX1, midY1, r, g, b);
}
}
procedure main() {
cls();
shading();
float x1 = -0.5;
float y1 = -0.5;
float x2 = 0.5;
float y2 = -0.5;
float x3 = 0.0;
float y3 = 0.5;
int level = 4;
koch(x1, y1, x2, y2, level, 1.0, 0.0, 0.0);
koch(x2, y2, x3, y3, level, 0.0, 1.0, 0.0);
koch(x3, y3, x1, y1, level, 0.0, 0.0, 1.0);
sierpinski(x1, y1, x2, y2, x3, y3, level, 1.0, 0.0, 0.0);
waitkey();
}
EndScript```
In this version of the program, we've combined the Koch snowflake fractal with the Sierpinski triangle and added some color to create a more harmonious and visually interesting fractal. The `koch` procedure is the same as before, but we've added a new `sierpinski` procedure that recursively subdivides a triangle and removes its center to create the Sierpinski triangle pattern.
In the `main` procedure, we first draw the Koch snowflake fractal using the `koch` procedure with different colors for each side of the triangle. We then call the `sierpinski` procedure to create the Sierpinski triangle pattern inside the Koch snowflake, using the same colors as the corresponding sides of the snowflake.
When you run this program, you should see a Koch snowflake fractal with harmonious colors and a Sierpinski triangle pattern inside it. You can experiment with different values of the `level` variable to create different variations of the fractal and the Sierpinski triangle pattern.