Full Spectrum Spirograph
Create a New Document:
Create a new document for print (8.5 X 11).
Open the Color Palette:
Locate the color swatch group you will use for this activity. On the color swatch palette click the Swatch Library menu button on the bottom left side of the Swatches palette.
This shows the available swatch palettes. Choose Scientific > Analogous:
The Scientific Analogous color palette should now appear in your document:
Turn on Smart Guides:
Make sure to turn on Smart Guides: View > Smart Guides. To switch them on and off use ctrl + U. It is also recommend to turn on Snap to Point: View > Snap to Point. They will have a check beside them if they are turned on as shown below:
Create the Shape to Duplicate:
Draw a circle using the Ellipse tool 
, while holding down the Shift key. This will make your circle perfectly round. Fill the circle with the first color in the color palette.
Select the circle at the middle left point, hold down the Shift + Alt key and drag/duplicate the circle. Drag the circle to the right until you reach the center point of the original circle. Release the mouse.
Select both circles, go to the Pathfinder palette and click the Intersect option.
Your two circles intercepted should now look like this:
Go to the Transparency palette and adjust the value of 100 to 25. Change the mode from normal to Multiply. This will give your shape a lighter transparent color.
Select the Rotate Tool 
and while hold down the Alt key click exactly on the most bottom anchor point of the shape.
This opens the rotate dialog box. Enter a value of 10 as degrees (360°/36) and click the copy button.
Fill the duplicated shape with the next color in the color swatch fill.
Transform Again:
Now the fun part can begin. With the 2nd circle selected, hit ctrl + D to repeat the exact transformation. Give the 3rd shape the 3rd swatch fill. Hit ctrl + D again. Give the 4th shape the 4th swatch fill. Continue until you have formed a complete circle.
Keep repeating the steps until the spirograph is complete.
