Jerry Leventer

Spirograph Geometric Graphic Design Demo – Try It Here!

February 16th, 2009 · 5 Comments · Fun & Recreation

What is a Spirograph?
by Anu Garg

A Spirograph is a curve formed by rolling a circle inside or outside of another circle. The pen is placed at any point on the rolling circle. If the radius of fixed circle is R, the radius of moving circle is r, and the offset of the pen point in the moving circle is O, then the equations of the resulting curve is defined by:

x = (R+r)*cos(t) – O*cos(((R+r)/r)*t)
y = (R+r)*sin(t) – O*sin(((R+r)/r)*t)
(moving circle outside the fixed circle)

x = (R-r)*cos(t) + O*cos(((R-r)/r)*t)
y = (R-r)*sin(t) – O*sin(((R-r)/r)*t)
(moving circle inside the fixed circle)


How to use it?

Here is how you can use the controls in this Spirograph applet:

  • The first three scroll bars in the control panel let you change R, r and O respectively.
  • You can use the next three scroll bars to change the color of the drawing. These scroll bars change the red, green and blue values of the color (in the range 0-255) respectively.
  • The last scroll bar lets you choose the number of iterations for the Spirograph. Move it to beginning and then slowly increase it to see how many iterations it takes to complete the spirograph.
  • You can use the Random button to select random values for the radii and color.

Created by Anu Garg.

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5 responses so far ↓

  • 1 dubli scam // Apr 28, 2009 at 3:28 am

    That is a cool design. I wonder if the aliens use this technique on their crop circles…

  • 2 Jerry Leventer // Apr 28, 2009 at 10:47 am

    So, that’s how they do it! LOL

  • 3 Web Design West Lothian // Dec 9, 2009 at 1:45 pm

    Lot’s of fun!

    The kids love playing with that sort of stuff.

  • 4 Business // Jun 29, 2010 at 6:45 pm

    Spirographs are used to produce wave pattern drawings, especially when a circular cog moves around the inside or outside of a circle. Different shapes can be produced by changing the shapes and sizes of a cog and the shape in or around which it moves.

  • 5 Sourav Chakraborty // Feb 11, 2011 at 9:30 am

    I used to have soo much fun with this things when I was a kid. And even now, I find them very interesting.
    Just noticed one thing: the ‘densest’ drawings come from two relatively prime radius (may be it is too obvious to you).

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