I should point out that this is just one way of how you can create these kind of compositions. I'm sure there are other techniques as well. This shape is inspired by Andy's creation and recreated for education purposes only. Don't copy his work, but explore the technique more and create different compositions. For this tutorial I've tried to find a simple way, so I can explain things in an easy and understandable manner, inviting you to go further and do some amazing stuff yourself.
Prepare color palette
First you'll need to do some preparation work. For this shape we need to create 36 color swatches going from bright yellow, to orange, red, purple, blue, green. Keep in mind that there should be a smooth transition between each color swatch. Make sure the very last yellow-green swatch will give a smooth transition to the first yellow swatch.
Create the shape to duplicate
Draw a circle using the Ellipse tool, holding down the Shift key. Give the circle a bright yellow fill. Make sure to turn on Smart Guides: View > Smart Guides. To switch them on and off use cmd/ctrl + U. It is also recommended to turn on Snap to Point: View > Snap to Point.
Select the circle at the center left point, hold down the Shift + Alt/Option 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. (For CS3, please hold down the Alt/Option key or click the Expand button after you have clicked.) You should now end up with a shape as shown in the image below.
Adjust transparency value and mode
Go to the Transparency palette and adjust the value of 100 to 25. Change the mode from normal to Multiply.
Start rotating and duplicating the shape
Select the Rotate Tool (R), hold down the Option/Alt key and click exactly on the most bottom anchor point of the shape. Enter a value of 10 as degrees (360°/36) and click the copy button. Give the duplicated shape the 2nd (yellow) swatch fill.
Now the fun part can begin. With the 2nd circle selected, hit cmd/ctrl + D to repeat the exact transformation. Give the 3rd shape the 3rd swatch fill. Hit cmd/ctrl + D again. Give the 4th shape the 4th swatch fill. Repeat these steps: cmd/ctrl + D, apply next swatch as fill.
Keep repeating the steps until the spirograph is complete.
Respect the creator and his work
Being inspired by his work or his technique is fine, but do not steal or copy. Inspiration should lead to new ideas, new creations. I invite you to experiment with different shapes, different patterns or try out different angles and color combinations. All Andy's work is copyright protected and may not be copied or used in any way without his permission. Don't make Andy regret giving me permission to write this tutorial. Respect!
Result of my experimentation
I thought, since I always stress out experimentation is vital, I share what I've created. Once I was playing around with this Transform Again technique, I was thinking why not try out Transform Each instead and see where I end up. Here is the result of some of my experimentations :
Start with 3 overlapping circles. Draw one and rotate/duplicate the circle at 120°. Group the circles and copy, rotate at 48°, 2 times in a row. You end up with 3 circles shapes in total (each shape containing 3 circles). I've used different colors (radial gradients) for each with different transparency values and transparency modes.
Start with a triangular shape. Copy, rotate at 18°, 6 times in a row. You end up with 7 triangle shapes in total. I've used different colors with an opacity of 100% in Screen mode. This way the overlapping area in the center is white.
Start with the same triangular shape. Copy, rotate at 12°, scale at 115% and move -10 mm horizontally and 10 mm vertically, 10 times in a row. You end up with 11 triangle shapes in total. I've used different colors with an opacity of 40% in Multiply mode.
Start with a simple square. Copy and rotate at -10° and scale 85%, 8 times in a row. You end up with 9 squares in total. Then rotate the entire shape at -10°. Use 10% opacity in Multiply mode.
This article has been originally published in 2009.