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Chris Greening
Chris Greening

Posted on • Updated on • Originally published at

Configuring the Spyrograph trace method to explore stunning geometric visualizations in Python

DISCLAIMER: This blog post was written by a human with the help of AI

Hypotrochoids and epitrochoids are fascinating mathematical curves that create beautiful, mesmerizing patterns

The spyrograph Python package, built on top of the turtle library, provides an easy-to-use interface for visualizing these captivating curves

In this blog post we'll explore how we can customize the trace method to create our own highly configurable generative art pieces

Table of Contents

GitHub logo chris-greening / spyrograph

Python library for analyzing, exploring, and visualizing epitrochoids and hypotrochoids in just a few lines of code

spyrograph: elegant mathematics and geometries

Animation of three geometric, symmetrical shapes being drawn next to one another left to right. The shape on the left is red, the middle green, and the right is blue.

What is it?

spyrograph is a lightweight Python package that provides an expressive and flexible set of tools for drawing beautiful mathematically driven art. With just a few lines of easy-to-read code you can start analyzing, visualizing, and exploring elegant mathematics

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Table of Contents

πŸ”‘ Key features

  • Expressive and consistent syntax
  • Robust underlying mathematics
  • Beginner and expert friendly
  • numpy is the only required third-party installation
  • Clear visualizations and animations
  • Flexible to a wide range of usecases
  • Lightweight, just plug and play

Sample hypotrochoid drawing showing a circle rolling around the interior of another circle drawing a geometric shape

πŸ’» Installation


Install the latest stable release from PyPI using

$ pip3 install spyrograph
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or clone the development version from GitHub with

$ git clone
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🌱 Quickstart

spyrograph is designed to be expressive and easy-to-use - simply import spyrograph and jump right into drawing elegant, complex shapes…

Getting started

To begin, we'll need to install the spyrograph package. You can do this by running the following command:

pip3 install spyrograph
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Once you have the package installed, let's import the Hypotrochoid class to trace our shape:

from spyrograph import Hypotrochoid
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Using the trace method

The trace method is one of the centerpieces of the spyrograph package, allowing users to draw beautiful hypotrochoids and epitrochoids with ease

And to top it off the method comes with a variety of customization options, enabling users to create unique patterns suited to their usecase

Here's a simple example to get us started:

import numpy as np

# Instantiate our hypotrochoid
thetas = np.arange(0, 2 * np.pi, 0.05)
hypotrochoid = Hypotrochoid(R=200, r=50, d=50, thetas=thetas)

# Draw the hypotrochoid using the trace method
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Tracing of a shape with a simple line with 4 cusps roughly in the shape of a diamond

This code snippet will create a hypotrochoid with the specified parameters and trace it on the turtle screen

You can experiment with different values for R, r, d, and thetas to create a wide variety of patterns and shapes

Customizing the visualization

The trace method offers a wide range of customization options to suit our usecase as needed

Here's an example of how to modify various aspects of the visualization:

    screen_size=(800, 800),
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A circle rolling around the inside of another circle traces the same diamond shape as previous but this time the color is red and we can see the animation drawing in real-time

In this example, we have:

  • Set the screen size to 800x800 pixels
  • Changed the background color to black
  • Used red as the color of the primary tracing
  • Displayed the inner and outer circles that compose the trace
  • Show the full path that will be traced
  • Set the color of the pre-drawn path to grey
  • Set the color of the circles to white
  • Added a 0.01 second pause for each frame
  • Set the animation to repeat infinitely


The spyrograph Python package empowers users to create and customize mesmerizing hypotrochoids and epitrochoids with just a few lines of code

By leveraging the trace method and its customization options, we can easily generate an array of captivating patterns and stunning art pieces

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