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Mcworter dendrite fractal

World's simplest fractal tool

This utility lets you draw your own original McWorter dendrite fractals. You can choose between four dendrite types – pentadendrite, hexadendrite, octadendrite and a single dendrite branch. There are also two extra drawing modes available – the starfish fractal mode and open fractal mode that create even more possibilities (see description below for more details). You can adjust the size and color of the drawing canvas and set its padding. You can also adjust the number of iterations, choose the rotation of the fractal (clockwise or counterclockwise), and its direction (right, left, up or down). Finally, you can choose the thickness of the fractal curve, adjust its color, and fill the inside of the fractal with any color. Fun fact – the McWorter fractal consists of a set of six-fold zigzags that don't overlap and have a 5-fold symmetry. Fractabulous!
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Dendrite Fractal Types
Draw the fractal from five dendrites.
Draw the fractal from six dendrites.
Draw the fractal from eight dendrites.
Draw the fractal from a single dendrite.
Iterations, Size and Modes
Dendrite's iterative depth.
Width.
Height.
Draw dendrites pointing inside the polygon. (Create an anti-dendrite.)
Make a gap between the dendrites.
The angle of fractal's gap.
Colors, Line and Frame
Canvas fill color.
Dendrite curve color.
Dendrite fill color.
Curve width.
Padding.
Dendrite fractal's rotation.
Dendrite fractal's direction.
Mcworter dendrite fractal tool What is a mcworter dendrite fractal?
This online browser-based tool creates unique and colorful McWorter dendrite fractals. The McWorter dendrite fractals are a family of symmetric and self-similar fractals that consists of dendrite subfractals. The dendrite curve is a variation of McWorter's pentigree (short for pentagon filigree). It's constructed from a zig-zag of six segments, which are bent at angles of 72, 72, 144 (2x72), 72, and 72 degrees. The fractal starts with a unit segment and with each step, each segment is replaced with this zigzag. If this process is repeatedly iterated, then a dendrite fractal is formed. McWorter's pentadendrite is formed by sequentially connecting five copies of the dendrite curve that are pointing outside the pentagon. Similarly, the hexadendrite and octadendrite are a connection of six and eight dendrites. Dendrites can also be connected in such a way that they point inside the polygon. This case is illustrated if the "Starfish Mode" option is enabled. This mode reverses the direction of dendrite fibers and creates a starfish fractal. The "Open Mode" cuts the fractal open and creates a gap between the dendrites. This fractal (just like many others) was discovered by accident by William A. McWorter as he was experimenting with a BASIC program that generates dragon curves. Mind blowing and ingenious at the same time, or as we love to say – fractabulous!
Mcworter dendrite fractal examples Click to use
Pentadendrite Fractal
In this example, we generate the McWorter's pentadentrite fractal, which is created from five touching dendrites pointing outside the pentagon. We set the rotation of the fractal to counterclockwise and generate the fifth iteration step on a Koamaru deep blue color canvas of 600 by 600 pixels.
In this example, we generate the McWorter's pentadentrite fractal, which is created from five touching dendrites pointing outside the pentagon. We set the rotation of the fractal to counterclockwise and generate the fifth iteration step on a Koamaru deep blue color canvas of 600 by 600 pixels.
Required options
These options will be used automatically if you select this example.
Draw the fractal from five dendrites.
Dendrite's iterative depth.
Width.
Height.
Draw dendrites pointing inside the polygon. (Create an anti-dendrite.)
Make a gap between the dendrites.
Canvas fill color.
Dendrite curve color.
Dendrite fill color.
Curve width.
Padding.
Dendrite fractal's rotation.
Dendrite fractal's direction.
Starfish Pentadendrite
This example applies the "Starfish Mode" to the pentadentrite fractal. In this case, all five dendrites point inside the pentagon and as a result, we get a fractal that is very similar to a starfish! We draw a 4th order curve on a Malibu color canvas, using a black line and golden-fizz color fill.
This example applies the "Starfish Mode" to the pentadentrite fractal. In this case, all five dendrites point inside the pentagon and as a result, we get a fractal that is very similar to a starfish! We draw a 4th order curve on a Malibu color canvas, using a black line and golden-fizz color fill.
Required options
These options will be used automatically if you select this example.
Draw the fractal from five dendrites.
Dendrite's iterative depth.
Width.
Height.
Draw dendrites pointing inside the polygon. (Create an anti-dendrite.)
Make a gap between the dendrites.
Canvas fill color.
Dendrite curve color.
Dendrite fill color.
Curve width.
Padding.
Dendrite fractal's rotation.
Dendrite fractal's direction.
Hexadendrite Fractal
In this example, we generate a hexadendrite fractal and make the dendrites grow outside the hexagon. As there the hexagon has six sides, the dendrites are much more spread apart and the space that is formed inside the fractal is shaped like gecko lizard's fingers. We draw 5 iterations on a Klein-blue color background and fill gecko's paws with a Harlequin-green color.
In this example, we generate a hexadendrite fractal and make the dendrites grow outside the hexagon. As there the hexagon has six sides, the dendrites are much more spread apart and the space that is formed inside the fractal is shaped like gecko lizard's fingers. We draw 5 iterations on a Klein-blue color background and fill gecko's paws with a Harlequin-green color.
Required options
These options will be used automatically if you select this example.
Draw the fractal from six dendrites.
Dendrite's iterative depth.
Width.
Height.
Draw dendrites pointing inside the polygon. (Create an anti-dendrite.)
Make a gap between the dendrites.
Canvas fill color.
Dendrite curve color.
Dendrite fill color.
Curve width.
Padding.
Dendrite fractal's rotation.
Dendrite fractal's direction.
Octadendrite Fractal
It this example, we draw three clockwise recursions of an octadendrite fractal on a 600x600px canvas with 10px padding. This fractal consists of eight dendrite fibers that connect at an angle of 45 degrees. This construction makes it look a bit similar to the Koch snowflake fractal.
It this example, we draw three clockwise recursions of an octadendrite fractal on a 600x600px canvas with 10px padding. This fractal consists of eight dendrite fibers that connect at an angle of 45 degrees. This construction makes it look a bit similar to the Koch snowflake fractal.
Required options
These options will be used automatically if you select this example.
Draw the fractal from eight dendrites.
Dendrite's iterative depth.
Width.
Height.
Draw dendrites pointing inside the polygon. (Create an anti-dendrite.)
Make a gap between the dendrites.
Canvas fill color.
Dendrite curve color.
Dendrite fill color.
Curve width.
Padding.
Dendrite fractal's rotation.
Dendrite fractal's direction.
Open Pentadendrite
In this example, we apply the "Open Mode" to the pentadendrite fractal. As a result, we get a 15-degree opening between the first and last dendrites. In this drawing mode, the fractal can't be filled as it's not connected.
In this example, we apply the "Open Mode" to the pentadendrite fractal. As a result, we get a 15-degree opening between the first and last dendrites. In this drawing mode, the fractal can't be filled as it's not connected.
Required options
These options will be used automatically if you select this example.
Draw the fractal from five dendrites.
Dendrite's iterative depth.
Width.
Height.
Draw dendrites pointing inside the polygon. (Create an anti-dendrite.)
Make a gap between the dendrites.
The angle of fractal's gap.
Canvas fill color.
Dendrite curve color.
Dendrite fill color.
Curve width.
Padding.
Dendrite fractal's rotation.
Dendrite fractal's direction.
A Dendrite Fiber
This example shows an individual dendrite subfractal fiber at its 5th iteration that all other fractals are made out of. At 72 degrees it has 5-fold symmetry creates a pentadentrite, at 60 degrees it has 6-fold symmetry and creates a hexadentrite and at 45 degrees it has 8-fold symmetry and creates an octadentrite. It also has several other symmetries that are less interesting.
This example shows an individual dendrite subfractal fiber at its 5th iteration that all other fractals are made out of. At 72 degrees it has 5-fold symmetry creates a pentadentrite, at 60 degrees it has 6-fold symmetry and creates a hexadentrite and at 45 degrees it has 8-fold symmetry and creates an octadentrite. It also has several other symmetries that are less interesting.
Required options
These options will be used automatically if you select this example.
Draw the fractal from a single dendrite.
Dendrite's iterative depth.
Width.
Height.
Draw dendrites pointing inside the polygon. (Create an anti-dendrite.)
Make a gap between the dendrites.
The angle of fractal's gap.
Canvas fill color.
Dendrite curve color.
Dendrite fill color.
Curve width.
Padding.
Dendrite fractal's rotation.
Dendrite fractal's direction.
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-mcworter-dendrite-fractal?&width=600&height=600&iterations=5&background-color=%23171594&line-segment-color=white&fill-color=%23336699&line-width=3&padding=10&pentadendrite=true&starfish-mode=false&open-mode=false&rotation=counterclockwise&direction=up
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