 # Levy fractal

## World's simplest fractal tool

This utility lets you draw colorful and custom Levy fractals. You can choose between four Levy fractal types (Levy dragon, two types of Levy tapestry and Levy diamond) and recursively iterate them for any number of times. You can customize the space for drawing, too. In particular, you can choose your own color for the canvas and adjust its height, width, and padding. You can also choose the fractals' spatial orientation and adjust the color and width for drawing the Levy curve. Fun fact – the Levy fractal consists of smaller Levy fractals that partially overlap each other. Fractabulous!
announcement a new project!
Super exciting news! We just launched MATHURLS – a fun math news reader. Check it out!
Levy Fractal Type
Draw the fractal from two edges of an equilateral triangle.
Draw the fractal from curves pointing outside the square.
Draw the fractal from curves pointing inside the square.
Draw the fractal from a 3-sided trapezoid.
Depth, Size and Orientation
Levy fractal's recursive depth.
Space width.
Space height.
Levy fractal's orientation.
Line and Colors
Levy line's thickness.
Levy line's color.
Background color.
Levy fractal tool What is a levy fractal?
This online browser-based tool allows you to create your own personal Levy fractals. The Levy fractal was first described by the Italian mathematician Ernesto Cesaro in 1906 and the German mathematician Georg Faber in 1910. However, it is named after the French mathematician Paul Levy, who was the first to describe its self-similar properties and estimate its Hausdorff dimension. Depending on the initial figure, there are four known types of the Levy fractal – Levy dragon, inside and outside Levy tapestry, and Levy diamond. The motif for the Levy dragon fractal is the two sides of an equilateral triangle and the basis is a unit line. At every next iteration, each line segment is replaced by the motif. The basis for the outside/inside Levy tapestry is a square and the motif is again the two sides of an equilateral triangle. To create the next iteration, the motifs are directed outside or inside of the square basis. The replacement figure for the Levy diamond is an isosceles trapezoid and the initial figure is a line. Each next iteration replaces every line in the fractal with the replacement figure. The Hausdorff dimension, which describes the complexity of the fractal for the Levy curve is almost the highest of all two-dimensional fractals and is very close to 2. That means this is one of the most chaotic and complex fractals there is. What's more, the interior of the Levy dragon consists of a countable number of components, the largest of which is a hexagon that is only a speck on the dragon. Mind blowing and ingenious at the same time, or as we love to say – fractabulous!
Levy fractal examples Click to use
Levy Dragon
In this example, we generate the regular Levy fractal (also known as Levy dragon) at its 12th iteration step. We draw the curve with a 3-pixel line on a rectangular canvas of size 900 by 600, with 15-pixel padding. Required options
These options will be used automatically if you select this example.
Draw the fractal from two edges of an equilateral triangle.
Levy fractal's recursive depth.
Space width.
Space height.
Levy fractal's orientation.
Levy line's thickness.
Levy line's color.
Background color.
Levy Tapestry on the Outside
This example draws an outside Levy tapestry fractal. This fractal begins as a square but with increasing recursions, it becomes an octagon. We generate 15th recursive steps using 1-pixel thick, cream color line and we draw it on a Monza color square canvas. Required options
These options will be used automatically if you select this example.
Draw the fractal from curves pointing outside the square.
Levy fractal's recursive depth.
Space width.
Space height.
Levy fractal's orientation.
Levy line's thickness.
Levy line's color.
Background color.
Levy Tapestry on the Inside
In this example, we have selected the "Inside Levy Tapestry" fractal type and generate 14 stages for it. As you can see, the curves for this type overlap, which is rare in fractals. We use a 600- by 600-pixel space, filled with black color. For the Levy tapestry, we use a golden fizz color line with a thickness of 2 pixels. Required options
These options will be used automatically if you select this example.
Draw the fractal from curves pointing inside the square.
Levy fractal's recursive depth.
Space width.
Space height.
Levy fractal's orientation.
Levy line's thickness.
Levy line's color.
Background color.
Levy Diamonds
In this example, we generate the Levy diamonds fractal, which is drawn from a 3-sided equal trapezium with a 30-degree angle at the base. We display 10 recursive steps of the Levy diamond curve on a vivid violet 900px-by-600px area. Required options
These options will be used automatically if you select this example.
Draw the fractal from a 3-sided trapezoid.
Levy fractal's recursive depth.
Space width.
Space height.
Levy fractal's orientation.
Levy line's thickness.
Levy line's color.
Background color.
Detailed Levy Tapestry
In this example, we generate only 8 iterations of the Levy tapestry to clearly illustrate how the fractal evolves. We use an 8-pixel thick drawing pen so that all lines were well visible and draw them in contrasting colors (green-yellow color pen on a navy blue background.) Required options
These options will be used automatically if you select this example.
Draw the fractal from curves pointing inside the square.
Levy fractal's recursive depth.
Space width.
Space height.
Levy fractal's orientation.
Levy line's thickness.
Levy line's color.
Background color.
Inverted Levy Curve
In this example, we invert the orientation of the Levy dragon fractal and turn it upside down. We use a Shalimar-yellow color line on a Christine-orange color background and show the 10th recursive stage. Required options
These options will be used automatically if you select this example.
Draw the fractal from two edges of an equilateral triangle.
Levy fractal's recursive depth.
Space width.
Space height.
Levy fractal's orientation.
Levy line's thickness.
Levy line's color.
Background color.
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!
All fractal tools
Didn't find the tool you were looking for? Let us know what tool we are missing and we'll build it!
Quickly draw a custom McWorter dendrite fractal.
Quickly draw a custom canopy tree fractal.
Quickly draw a custom Gosper fractal.
Quickly draw a custom Z-order fractal.
Quickly draw a custom Hilbert fractal.
Quickly draw a custom binary v-fractal.
Quickly draw a custom Peano fractal.
Quickly draw a custom Heighway dragon fractal.
Quickly draw a custom twin dragon Heighway fractal.
Quickly draw a custom Heighway nonadragon fractal.
Quickly draw a custom Koch fractal.
Quickly draw a custom triflake fractal.
Quickly draw a custom Sierpinski triangle fractal.
Quickly draw a custom Sierpinski pentagon fractal.
Quickly draw a custom Sierpinski hexagon fractal.
Quickly draw a custom Sierpinski polygon fractal.
Quickly draw a custom Moore fractal.
Quickly draw a custom Cantor comb fractal.
Quickly draw a custom Cantor dust fractal.
Quickly draw a custom Levy fractal curve.
Quickly draw a custom ice fractal.
Quickly draw a custom Pythagoras tree fractal.
Quickly draw a custom t-square fractal.
Quickly draw a custom Hausdorff tree fractal.
Coming soon These fractal tools are on the way
Generate a Hilbert Sequence
Walk the Hilbert fractal and enumerate its coordinates.
Generate a Peano Sequence
Walk the Peano fractal and enumerate its coordinates.
Generate a Moore Sequence
Walk the Moore fractal and enumerate its coordinates.
Generate a Cantor String
Encode the Cantor set as a string.
Mandelbrot Tree
Generate a Mandelbrot tree fractal.
Barnsey's Tree
Generate a Barnsley's tree fractal.
Barnsey's Fern
Generate a Barnsley's fern fractal.
Binary Fractal Tree
Generate a binary tree fractal.
Ternary Fractal Tree
Generate a ternary tree fractal.
Dragon Fractal Tree
Generate a dragon tree fractal.
De Rham Fractal
Generate a de Rham curve.
Takagi Fractal
Generate a Takagi-Landsberg fractal curve.
Peano Pentagon
Generate a Peano pentagon fractal curve.
Tridendrite Fractal
Generate a tridendrite fractal curve.
McWorter's Pentigree
Generate a Pentigree fractal curve.
McWorter's Lucky Seven
Generate a lucky seven fractal curve.
Eisenstein Fractions
Generate an Eisenstein fractions fractal curve.
Bagula Double V
Generate a Bagula double five fractal curve.
Julia Set
Generate a Julia fractal set.
Mandelbrot Set
Generate a Mandelbrot fractal set.
Toothpick Fractal
Generate a toothpick sequence fractal.
Ulam-Warburton Fractal
Generate an Ulam-Warburton fractal curve.