Back to Basics - Sierpinski Triangle
I remember back when I was first learning C, and one of the assignments was to draw the Sierpinski Triangle. I didn’t know what it was, but sequential steps were given to iteratively create it. The steps were roughly like so:
- Generate a triangle on a plane with 3 points
- Set the centre of the triangle as the current point
- Randomly select one of the triangle points
- Get the mid-point between the current point and the selected point
- Plot the mid-point and set it as the current point
- Randomly select one of the triangle points
- Get the mid-point between the current point and the selected point
- Plot the mid-point and set it as the current point
- Continue till iteration limit is reached
I was told to visualise the plane as a matrix, and the plotted points were to be printed as asterisks on the screen.
It’s been years now, and I still think the screen output of my Sierpinski Triangle sucked because of the low resolution. Now, older and wiser, I can come up with a better representation.
Download the full source code.
using System; using System.Collections.Generic; using System.Text; using System.Drawing; namespace b2bSierpinskiTriangle { class Program { static void Main(string[] args) { const int cnSize = 512; const int cnLimit = 50000; int[,] points = new int[3, 2]; points[0, 0] = cnSize / 2; points[0, 1] = 10; points[1, 0] = 10; points[1, 1] = cnSize - 16; points[2, 0] = cnSize - 16; points[2, 1] = cnSize - 16; Bitmap bm = new Bitmap(cnSize, cnSize); Graphics g = Graphics.FromImage(bm); g.FillRectangle(Brushes.White, 0, 0, cnSize, cnSize); int trianglepoint = 0; Random rand = new Random(); int currentx = 0, currenty = 0; int previousx = cnSize / 2, previousy = cnSize / 2; for (int i = 0; i < cnLimit; ++i) { trianglepoint = rand.Next(3); currentx = (points[trianglepoint, 0] + previousx) / 2; currenty = (points[trianglepoint, 1] + previousy) / 2; bm.SetPixel(currentx, currenty, Color.Navy); previousx = currentx; previousy = currenty; } bm.Save("sierpinski.bmp"); g.Dispose(); bm.Dispose(); } } }
Short and sweet. Instead of printing to the command line screen, I plotted the points to a bitmap. I still remember printing my program listing and the Sierpinski asterisks output. Though pleased with the required output, I thought it looked a little unrefined around the edges.
Printing to a bitmap at pixel level makes it look much better…
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[...] usual problems fall into topics like finding shortest path with Dijkstra, drawing the Sierpinski Triangle, or manipulating huge matrices for LU decomposition or QR decomposition (killed lots of brain cells [...]