The sierpiński triangle sometimes spelled sierpinski also called the sierpiński gasket or sierpiński sieve is a fractal attractive fixed set with the overall shape of an equilateral triangle subdivided recursively into smaller equilateral triangles.
What is sierpinski s carpet.
The sierpinski carpet is the intersection of all the sets in this sequence that is the set of points that remain after this construction is repeated infinitely often.
Take the remaining 8 squares.
The sierpinsky carpet is a self similar plane fractal structure.
Divide each one into 9 equal squares.
Step through the generation of sierpinski s carpet a fractal made from subdividing a square into nine smaller squares and cutting the middle one out.
You keep doing it as many times as you want.
The sierpinski triangle i coded here.
The figures below show the first four iterations.
What is the area of the figure now.
Remove the middle one from each group of 9.
The carpet is one generalization of the cantor set to two dimensions.
The technique of subdividing a shape into smaller copies of itself removing one or more copies and continuing recursively can be extended to other shapes.
Here are 6 generations of the fractal.
Originally constructed as a curve this is one of the basic examples of self similar sets that is it is a mathematically generated.
Sierpinski s carpet also has another very famous relative.
Explore number patterns in sequences and geometric properties of fractals.
The area of sierpinski s carpet is actually zero.
The squares in red denote some of the smaller congruent squares used in the construction.
Creating one is an iterative procedure.
Sierpinski s carpet take a square with area 1.
Remove the middle one.
To construct it you cut it into 9 equal sized smaller squares and remove the central smaller square from all squares.
This is a fun little script was created as a solution to a problem on the dailyprogrammer subreddit community.
This tool lets you set how many cuts to make number of iterations and also set the carpet s width and height.
Start with a square divide it into nine equal squares and remove the central one.
How to construct it.
Another is the cantor dust.
Here s the wikipedia article if you d like to know more about sierpinski carpet.
The sierpiński carpet is the fractal illustrated above which may be constructed analogously to the sierpiński sieve but using squares instead of triangles it can be constructed using string rewriting beginning with a cell 1 and iterating the rules.
For instance subdividing an equilateral triangle.
Divide it into 9 equal sized squares.
