# Z-order curve generator

## World's simplest math tool

Free online Z-order curve generator. Just press a button and you'll automatically get a Morton Z-curve. There are no ads, popups or nonsense, just an awesome Morton curve generator. Press a button, get a Z-curve. Created by math nerds from team Browserling.

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Z-order curve generator tool
What is a z-order curve generator?

This tool draws a Z-order curve, also known as Morton curve or Lebesgue curve. A Z-curve is a fractal space-filling structure that has a Z-shaped form. It is a continuous curve consisting of a sequence of connected letters Z. In this tool, you can change the look of the Morton code curve by changing the number of fractal iterations, curve width, padding, size and color. Currently, we have set a limit of 10 iterations because the 11th iteration takes too long to calculate. Mathabulous!

Z-order curve generator examples
Click to use

Green Z-Curve

This example generates a Morton code curve using 5 iterations and sets background color to green. The curve color is black and there's a 5px padding around the curve.

**Required options**

Morton curves's width.

Morton curves's height.

Number of iterations.

Z-curve's background color.

Z-curve's line color.

Z-order curve's width.

Padding around Z-order curve.

Vertical Morton Curve

This example draws a rectangular Morton curve with vertically rotated Z letters. The height is 700px and the width is 500px. It also sets iterations to 3, padding to 15px, and width of curve's line to 7px.

**Required options**

Morton curves's width.

Morton curves's height.

Number of iterations.

Z-curve's background color.

Z-curve's line color.

Z-order curve's width.

Padding around Z-order curve.

64 Letters Z

In this example, we set the number of iterations to 4 that results in 64 letters Z. All Z's are interconnected by lines and a continuous curve forms that passes through all Z's from the first one to the last.

**Required options**

Morton curves's width.

Morton curves's height.

Number of iterations.

Z-curve's background color.

Z-curve's line color.

Z-order curve's width.

Padding around Z-order curve.

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-z-order-curve?&width=400&height=400&iterations=5&background-color=%23b7ff8a&line-segment-color=black&line-width=3&padding=5&direction=horizontal

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Quickly generate a Morton Z-order fractal curve.

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