Title: Draw a curlicue fractal in C#
For information about how this fractal works, see Curlicue Fractal by Eric W. Weisstein from MathWorld, a Wolfram Web Resource.
The program starts by drawing a line segment in the direction of the X axis. It then iteratively calculates theta and phi using these equations:
theta(n + 1) = (theta(n) + 2 × Pi × S) mod (2 × Pi)
phi(n + 1) = (theta(n) + phi(n)) mod (2 × Pi)
For some irrational number S. At each step, the program draws a new line segment in the direction given by phi.
The following DrawCurlicue method draws 10,000 segments following these rules.
// Draw the curve.
private void DrawCurlicue(Graphics gr)
{
const int scale = 2;
gr.ScaleTransform(
scale,
scale,
MatrixOrder.Append);
gr.TranslateTransform(
picCanvas.ClientSize.Width / 2,
picCanvas.ClientSize.Width / 2,
MatrixOrder.Append);
double s = double.Parse(txtS.Text);
double theta, phi, x0, y0, x1, y1;
theta = 0;
phi = 0;
x0 = 0;
y0 = 0;
// Use a zerowidth pen so it draws as thin as possible
// even after scaling.
using (Pen thin_pen = new Pen(Color.Red, 0))
{
for (int i = 1; i <= 10000; i++)
{
x1 = x0 + Math.Cos(phi);
y1 = y0 + Math.Sin(phi);
gr.DrawLine(thin_pen, (float)x0, (float)y0,
(float)x1, (float)y1);
x0 = x1;
y0 = y1;
phi = (theta + phi) % (2 * Math.PI);
theta = (theta + 2 * Math.PI * s) % (2 * Math.PI);
}
}
}
Download the example to experiment with it and to see additional details.
