# Sierpinski fractal

## World's simplest fractal tool

This utility lets you draw colorful and custom Sierpinski fractals. You can adjust the parameters of the initial triangle, such as its color and size, and generate as many fractal iterations from it as you want. The size can be specified by adjusting the width and height of the space where the fractal is constructed, as well as adjusting padding from the edges of the drawing area. You can also choose the direction which the vertex of the triangle will be pointing and specify the thickness of triangles' border. There are three colors you can adjust – color for the drawing space, triangles' border, and internal fill of triangles. Fun fact - if you write the binomial coefficients in a pyramid shape (Pascal's triangle shape) and color all odd numbers with black color and even numbers with white color, then the Sierpinski triangle will form. Fractabulous!

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Sierpinski fractal tool
What is a sierpinski fractal?

This online browser-based tool allows you to create your own unique Sierpinski fractals. The Sierpinski fractal is one of the most popular fractals. Because of its triangular form and 3-fold symmetry, it's also known as Sierpinski triangle and it's constructed from the set of triangles. It was first created and researched by the Polish mathematician Wacław Franciszek Sierpinski in 1915, although the triangular patterns it creates had been encountered many centuries before. To get a Sierpinski fractal, you start with a solid triangle and in the first step of construction remove an inverted triangle from its center. You're left with three triangles. In the second step, you now remove three inverted triangles from the remaining three triangles. This process continues as long as necessary. The number of filled triangles at the nth iteration step is equal to 3ⁿ⁻¹, and their size is s×4¹⁻ⁿ, where s is the size of the initial triangle. The limiting shape has zero area but the sum of all triangle edges has infinite length. Mind blowing and ingenious at the same time, or as we love to say – fractabulous!

Sierpinski fractal examples
Click to use

Sierpinski Fractal from 27 Triangles

In this example, we generate a multi-colored Sierpinski fractal at its 4th iteration stage, which means that it's built from 3⁴⁻¹ = 3³ = 27 triangles. We draw the triangles in Daintree color, fill them with a bright turquoise color and use lavender-rose color for the canvas area of a size 600 by 600 pixels. We also set 10-pixel padding for the triangle.

**Required options**

Recursive depth of the fractal.

Width of the fractal.

Height of the fractal.

Drawing space's
background color.

Triangle edge color.

Triangle fill color.

Triangle edges' width.

Padding from the edges.

Inverted Sierpinski Fractal

This example uses a 2-pixel line to draw an upside-down Sierpinski triangle of depth 10. The tiny triangles in the bigger triangle aren't filled with any color and are transparent. Only their border in a tolopea color is drawn on a twilight blue canvas.

**Required options**

Recursive depth of the fractal.

Width of the fractal.

Height of the fractal.

Drawing space's
background color.

Triangle edge color.

Triangle fill color.

Triangle edges' width.

Padding from the edges.

Filled Sierpinski Fractal

In this example, we form a Sierpinski fractal from filled triangles that are all connected by their vertices. We've left the border color empty so there's no color used for drawing the edges of triangles. We illustrate the sixth recursion step and there are 3⁶⁻¹ = 3⁵ = 243 triangles, each 1024 times smaller than the original triangle.

**Required options**

Recursive depth of the fractal.

Width of the fractal.

Height of the fractal.

Drawing space's
background color.

Triangle edge color.

Triangle fill color.

Triangle edges' width.

Padding from the edges.

Pro tips
Master online fractal tools

You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!

https://onlinefractaltools.com/draw-sierpinski-fractal?&width=600&height=600&iterations=4&background-color=%23ff8ce8&line-segment-color=%23022129&fill-color=%2311cef5&line-width=5&padding=10&direction=up

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