Scaling trochoid's and cycloid's input parameters with the Spyrograph `scale` method

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

In this blog post, we will explore the scale method in the spyrograph package which enables users to easily scale their trochoid's and cycloid's input parameters

• Scaling trochoid's and cycloid's input parameters with the spyrograph scale method
• Creating a Hypocycloid
• Scaling the Hypocycloid with the scale method
• Using scale to trace a beautiful pattern
• Conclusion

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

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

Official website

Official docs

Table of Contents

• Key features
• Installation
• Quickstart
• Contributing
• Blog posts
• Documentation
• License
• Support

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🔑 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

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💻 Installation

pip

Install the latest stable release from PyPI using

$ pip3 install spyrograph

or clone the development version from GitHub with

$ git clone https://github.com/chris-greening/spyrograph.git

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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…

View on GitHub

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Creating a Hypocycloid

First, let's create a Hypocycloid with 10 cusps to work with:

import numpy as np
from spyrograph import Hypocycloid

hypocycloid = Hypocycloid.n_cusps(
    R=300,
    n=10,
    thetas=np.arange(0, 2*np.pi, .1)
)

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Scaling the Hypocycloid with the scale method

Now that we have a Hypocycloid, we can easily scale it using the scale method:

scaled_hypocycloid = hypocycloid.scale(factor=.5)

The scaled_hypocycloid will now have its input parameters (R, r, and d) multiplied by the scaling factor

For example the radius of the big circle R=300 will now be R*.5=150

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Using scale to trace a beautiful pattern

Let's jump into a concrete example of using the scale method in action to trace a gradually smaller set of curves

from spyrograph import Hypocycloid
import numpy as np
import time

screen = None
hypocycloid = Hypocycloid.n_cusps(
    R=200,
    n=20,
    theta_start=0,
    theta_stop=2*3.1415,
    theta_step=.01
)
for i in range(1,40):
    screen = hypocycloid.trace(screen=screen)
    hypocycloid = hypocycloid.scale(factor=((40/(i+40))))
    time.sleep(.1)
turtle.exitonclick()

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Conclusion

The scale method in spyrograph provides a convenient way to resize trochoids and cycloids while preserving their shape

With just a single method call and a scaling factor, users can quickly create new shapes with different sizes, making the package even more versatile for artists, educators, and developers alike

Don't forget to experiment with different scaling factors and shapes to create stunning patterns and visuals!