Sierpinski triangle

The first few steps starting, for example, from a square also tend towards a Sierpinski triangle.

On every face there is a Sierpinski triangle and infinitely many are contained within.

A related construction making the figure similar to all three of its corner pieces produces the Sierpinski triangle.

In the following example, a function is defined and called (at the same time) to generate a Sierpinski triangle of depth 8.

There is another way to draw the Sierpinski triangle using an L-system.

Running the above program, for example, actually displays a Sierpinski triangle, which can be cut and pasted into another program.

The area of a Sierpinski triangle is zero (in Lebesgue measure).

One example is the Sierpinski triangle, where there are an infinite number of small triangles inside the large one.

The automaton "12/1" when applied to a single cell will generate four approximations of the Sierpinski triangle.

The Sierpinski triangle is an n-flake formed by successive flakes of three triangles.

The method of creation is rather similar to the ones used to create a Koch snowflake or a Sierpinski triangle.

Rule 102 reproduces the Sierpinski triangle.

An algorithm for obtaining arbitrarily close approximations to the Sierpinski triangle is as follows:

This program, taken from the Racket website, draws a Sierpinski triangle, nested to depth 8.

The Sierpinski triangle drawn using an L-system.

The canonical example is the Sierpinski gasket also called the Sierpinski triangle.

Sample programs include Sierpinski Triangle.

Here is how DrGeo can create a Sierpinski triangle recursively:

The canonical Sierpinski triangle uses an equilateral triangle with a base parallel to the horizontal axis (first image).

The name Tetrix is derived from the popular computer game Tetris and the fractal Sierpinski triangle.

Ternary numbers can be used to convey self-similar structures like the Sierpinski triangle or the Cantor set conveniently.

This is an attractive fixed set, so that when the operation is applied to any other set repeatedly, the images converge on the Sierpinski triangle.

Wacław Sierpiński describes the Sierpinski triangle.

For example, here is how a Sierpinski triangle can be made (as an IFS) with pykig:

More precisely, the limit as n approaches infinity of this parity-colored 2-row Pascal triangle is the Sierpinski triangle.