Sierpinski Gasket and Carpet Constructor v1.01 by S Kennedy, 9th June 2001

s_kennedy@lineone.net
http://website.lineone.net/~s_kennedy/index.htm


This is a small program created using Borland Delphi Developer v2. I originally created a similar program on an Amiga 1200 computer using AMOS basic while I was at university back in 1993 which I transfered to my PC in 1998. It has no real use except to display how the Sierpinski Gasket and Carpet can be created.

The Gasket is created by following a simple set of rules:

    1. Mark three points on a piece of paper that form an equilateral triangle. Label these A, B and C
    2. Draw a blue dot at A.
    3. Randomly choose one of the three lettered points and draw a dot halfway between the dot you just drew and the point chosen. Colour this dot blue if the randomly chosen point was A, green if the point chosen was B and red if it was C.
    4. Repeat step three as many times as you like.

Rather than ending up with a random set of colour dots as may be expected we actually get a self-similar shape that can be expressed mathematically as an infinite amount of triangles that have a combined surface area of zero.

For a closer look at the Sierpinski Gasket and a brief outline of the source code please vist my website at http://website.lineone/~s_kennedy/index.htm

The Sierpinski Carpet is similar except is based on squares and 8 suitable points have to been chosen initially. Step 3 then becomes Randomly choose one of the eight points and draw a dot two thirds of the way between the dot you just drew and the point chosen...


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Using the program

Choose which set you wish to draw using the Combo Box at the top of the Form. Press Start to clear the form and then plot 10000 points on the Form. Pressing Continue will add another 10000 plots to what is already on screen. Pressing Quit will allow you to choose the other set to draw.


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Version history

V1.01 		09.06.01 (Delphi v2)
		Added Start, Continue and Quit buttons (previously just clicked on main form)

V1.00		29.03.97 (Delphi v1)
		Re-written version of the programme I created in 1998. 

Original	1993 (AMOS Basic)