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 sierpiński carpet is a plane fractal first described by wacław sierpiński in 1916.
Originally constructed as a curve this is one of the basic examples of self similar sets that is it is a mathematically generated.
What is the area of the figure now.
Remove the middle one from each group of 9.
Divide it into 9 equal sized squares.
Sierpinski s carpet also has another very famous relative.
Here s the wikipedia article if you d like to know more about sierpinski carpet.
Creating one is an iterative procedure.
Start with a square divide it into nine equal squares and remove the central one.
This tool lets you set how many cuts to make number of iterations and also set the carpet s width and height.
It s a good practice to use virtualenvs to isolate package requirements.
Another is the cantor dust.
Explore number patterns in sequences and geometric properties of fractals.
A sierpinksi carpet is one of the more famous fractal objects in mathematics.
How to construct it.
Remove the middle one.
The carpet is one generalization of the cantor set to two dimensions.
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.
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.
This is a fun little script was created as a solution to a problem on the dailyprogrammer subreddit community.
To construct it you cut it into 9 equal sized smaller squares and remove the central smaller square from all squares.
You keep doing it as many times as you want.
Take the remaining 8 squares.
The sierpinski triangle i coded here.
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.
Divide each one into 9 equal squares.
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.
Here are 6 generations of the fractal.
For instance subdividing an equilateral triangle.
The squares in red denote some of the smaller congruent squares used in the construction.
The figures below show the first four iterations.
