# 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. Created by fractal fans from team Browserling. Fractabulous!

love math?
check out our math tools!

We also have Online Math Tools — utilities for doing mathy things. Check it out!

A link to this tool, including input, options and all chained tools.

Can't convert.

## What is a levy fractal?

learn more about this tool
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 useLevy 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**

Draw the fractal from two edges
of an equilateral triangle.

Levy fractal's recursive depth.

Space width.

Space height.

Padding around the fractal.

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**

Draw the fractal from curves
pointing outside the square.

Levy fractal's recursive depth.

Space width.

Space height.

Padding around the fractal.

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**

Draw the fractal from curves
pointing inside the square.

Levy fractal's recursive depth.

Space width.

Space height.

Padding around the fractal.

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**

Draw the fractal from a
3-sided trapezoid.

Levy fractal's recursive depth.

Space width.

Space height.

Padding around the fractal.

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**

Draw the fractal from curves
pointing inside the square.

Levy fractal's recursive depth.

Space width.

Space height.

Padding around the fractal.

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**

Draw the fractal from two edges
of an equilateral triangle.

Levy fractal's recursive depth.

Space width.

Space height.

Padding around the fractal.

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!

https://onlinefractaltools.com/draw-levy-fractal?&width=900&height=600&iterations=12&background-color=%231d2391&line-segment-color=white&line-width=3&padding=15&direction=up&levy-dragon=true

All fractal tools

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 Hilbert String

Encode the Hilbert fractal as a string.

Generate a Peano String

Encode the Peano fractal as a string.

Generate a Moore String

Encode the Moore fractal as a string.

Generate a Cantor String

Encode the Cantor set as a string.

Generate a Dragon String

Encode the Heighway Dragon as a string.

Generate a Sierpinski String

Encode the Sierpinski fractal as a string.

Sierpinski Pyramid

Generate a Sierpinski tetrahedron (tetrix) fractal.

Cantor's Cube

Generate a Cantor's cube fractal.

Menger Sponge

Generate a Sierpinski-Menger fractal.

Jerusalem Cube

Generate a Jerusalem cube fractal.

Mosely Snowflake

Generate a Jeaninne Mosely fractal.

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.

Mandelbulb Fractal

Generate a Mandelbulb fractal.

Mandelbox Fractal

Generate a Mandelbox fractal.

Buddhabrot Fractal

Generate a Buddhabrot fractal.

Burning Ship Fractal

Generate a Burning Ship fractal.

Toothpick Fractal

Generate a toothpick sequence fractal.

Ulam-Warburton Fractal

Generate an Ulam-Warburton fractal curve.

ASCII Fractal

Generate an ASCII fractal.

ANSI Fractal

Generate an ANSI fractal.

Unicode Fractal

Generate a Unicode fractal.

Emoji Fractal

Generate an emoji fractal.

Braille Fractal

Generate a braille code fractal.

Audio Fractal

Generate a fractal in audio form.

Draw a Pseudofractal

Create a fractal that looks like one but isn't a fractal.

Convert Text to a Fractal

Generate a fractal from any text.

Convert a String to a Fractal

Generate a fractal from a string.

Convert a Number to a Fractal

Generate a fractal from a number.

Merge Two Fractals

Join any two fractals together.

Draw a Random Fractal

Create a completely random fractal.

Iterate an IFS

Set up an arbitrary IFS system and iterate it.

Run IFS on an Image

Recursively transform an image using IFS rules.

Iterate an ICAF

Run infinite compositions of analytic functions.

Generate a Fractal Landscape

Create a surface that mimics a natural terrain.

Generate a Brownian Surface

Create a fractal surface via Brownian motion.

Generate a Self-similar Image

Apply fractal algorithms on your image and make it self-similar.

Find Fractal Patterns in Images

Find fractal patterns in any given image.

Find Fractal Patterns in Text

Find fractal patterns in any given text.

Find Fractal Patterns in Numbers

Find fractal patterns in any given number.

Fill a Plane with Fractals

Tessellate a plane with fractals.

Run a Cellular Automaton

Run a cellular automaton with custom rules.

Play Game of Life

Play Conway's Game of Life on an infinite grid.

Subscribe!
Never miss an update

Cool!

Notifications
We'll let you know when we add this tool

Cool!