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Sierpinski polyflake generator

World's simplest math tool

Free online Sierpinski polyflake fractal generator. Just press a button and you'll get a Sierpinski n-flake. There are no ads, popups or nonsense, just an awesome n-flake generator. Press a button – get a polyflake. Created by mathematicians for mathematicians.
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Size, Recursion and Sides
Polygon width.
Polygon height.
Number of recursive repetitions of the algorithm (iterations).
Number of basis polygon sides. (Must be at least 5.)
Polyflake Colors
Background color for polyflake.
Contour color for polyflake.
Fill color for polyflake.
Contour Width, Indent and Direction
Polygon contour thickness.
Indent in pixels around polygon.
In which direction to begin drawing the polygon?
Sierpinski polyflake generator tool What is a sierpinski polyflake generator?
This tool draws Sierpinski polyflakes. The Sierpinski polyflake, also known as a Sierpinski n-flake or Sierpinski n-gon is drawn by putting n regular polygons with n sides together vertex by vertex so that they don't overlap and form a closed circuit. With each iteration this fractal inscribes n new polygons in each of existing polygons using the same rule. This process can be recursively repeated for as many times as you've indicated in iterations option. For this fractal to work n has to be at least 5. You can specify the dimensions of the final n-flake and choose colors for it. Each inscribed polygon can be filled with any color and you can change polygon's border thickness, and select a color for it, too. You can choose four directions of motion for drawing the n-gon (up, down, right, left). And, optionally, you can make the polygon fit the entire canvas or indent it from the canvas. Mathabulous!
Sierpinski polyflake generator examples Click to use
Draw a Sierpinski Octagon
The basis of this example is an octagon (8-sided polygon). With each recursive iteration, each of original octagons is replaced with 8 new octagons. It uses 4 iterations (total of 8*8*8=512 octagons) and if you look very closely you can see that Koch snowflake forms in the center of every octagon.
Required options
These options will be used automatically if you select this example.
Polygon width.
Polygon height.
Number of recursive repetitions of the algorithm (iterations).
Number of basis polygon sides. (Must be at least 5.)
Background color for polyflake.
Contour color for polyflake.
Fill color for polyflake.
Polygon contour thickness.
Indent in pixels around polygon.
In which direction to begin drawing the polygon?
Draw an Inverted Sierpinski Pentagon
This example generates a Sierpinski 5-gon upside down for five iterations. Here the thickness of the contour around the n-flake is zero, so the fractal is drawn using two colors. The dimensions of canvas are 450x450px, but the actual figure size is reduced by 10px from all sides because of padding option.
Required options
These options will be used automatically if you select this example.
Polygon width.
Polygon height.
Number of recursive repetitions of the algorithm (iterations).
Number of basis polygon sides. (Must be at least 5.)
Background color for polyflake.
Contour color for polyflake.
Fill color for polyflake.
Polygon contour thickness.
Indent in pixels around polygon.
In which direction to begin drawing the polygon?
Draw a Sierpinski Tridecagon-flake
In this example, the fractal shape is similar to a circle because we use a 13-sided polygon as the basis. It uses 4 iterations and sets three colors – blue for the background, black for the contour, and red for the n-gon fill.
Required options
These options will be used automatically if you select this example.
Polygon width.
Polygon height.
Number of recursive repetitions of the algorithm (iterations).
Number of basis polygon sides. (Must be at least 5.)
Background color for polyflake.
Contour color for polyflake.
Fill color for polyflake.
Polygon contour thickness.
Indent in pixels around polygon.
In which direction to begin drawing the polygon?
Pro tips Master online math 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://onlinemathtools.com/generate-sierpinski-polyflake?&width=400&height=400&iterations=4&polygon=8&background-color=%23f0ff4b&line-segment-color=black&fill-color=%23049fff&line-width=3&padding=3&direction=left
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