What is a Spirograph?
A Spirograph is both a geometric drawing toy and the name for the beautiful patterns it creates. Introduced in 1965 by British engineer Denys Fisher, the Spirograph became one of the most beloved creative toys of the 20th century.
The physical toy consists of plastic gears and rings with teeth along their edges. By placing a pen through holes in the gears and rotating them inside or outside the rings, intricate geometric patterns emerge—each one unique based on the gear size, hole position, and placement method.
The Mathematics: Trochoids
The patterns created by Spirographs are mathematical curves called trochoids. More specifically:
Hypotrochoids are created when a smaller circle rolls inside a larger circle. The pen traces a path as it rotates within the fixed ring.
Epitrochoids are created when a smaller circle rolls outside a larger circle. The pen traces a path as it rotates around the exterior of the fixed ring.
Fun fact: The mathematical equations for these curves were studied long before Spirograph was invented! Mathematicians like Albrecht Dürer explored similar geometric constructions in the 16th century.
Why "Hypnotrochoid"?
The name Hypnotrochoid is a playful combination of "hypnotic" and "trochoid"—because let's be honest, watching these patterns emerge is mesmerizing. There's something deeply satisfying about the predictable-yet-surprising nature of mathematical curves unfolding before your eyes.
Nostalgia & Why This Was Built
For many of us who grew up in the 80s, 90s, and early 2000s, Spirograph was more than just a toy—it was a gateway to creative exploration and an early encounter with the beauty of mathematics.
This digital recreation captures that tactile joy while adding modern conveniences: multiple colors, adjustable line thickness, unlimited canvas space, and the ability to save your creations. It's a love letter to childhood creativity and the meditative flow state of making art through simple, repetitive motion.
Whether you're revisiting a cherished childhood toy or discovering Spirograph patterns for the first time, Hypnotrochoid invites you to slow down, experiment, and lose yourself in the hypnotic dance of gears and curves.
Design philosophy: Best experienced on desktop with a keyboard, just like the original required a steady hand and patience. The act of holding down arrow keys mimics the focused attention needed to guide a pen through the physical toy's gears.
How to Use Hypnotrochoid
Step 1: Place the Ring
Click the ring icon in the left panel, then click on the canvas to place it. The ring is your fixed outer boundary.
Step 2: Choose a Gear
Select one of the gears from the left panel. Different sized gears create different patterns.
Step 3: Position the Gear
Place the gear either inside the ring (for hypotrochoids) or outside the ring (for epitrochoids). The gear will snap to mesh perfectly with the ring's teeth.
Step 4: Select a Pen Hole
Click on one of the colored dots on the gear. This is where your virtual pen will be placed. Different holes create different curve sizes.
Step 5: Choose Your Style
Pick your color and line thickness from the bottom-left style picker. Pro tip: Thin lines often create the most elegant patterns!
Step 6: Draw!
Use the A and D keys (or scroll with your mouse) to rotate the gear and draw your pattern. Hold the keys to draw continuously.
Helpful hint: As you progress through these steps, the app will show contextual hints at the top of the screen telling you what to do next!