How to Create Vector Spirograph Designs

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I've been fascinated by Spirograph designs since I was a kid. I love the cool symmetrical way they look. I know there's programs out there that can draw Spirograph designs automatically, but that just isn't as fun as making them by hand.
When I started learning Illustrator, I struggled to make the loops manually and the results were far from perfect. I knew Illustrator must have a better way to do it, and eventually I found it! That's what it's all about, just learning to use the tools so that your ideas can be set free.
Below is the final design we will be working towards.
Go to Edit - Preferences - General and make sure Scale Strokes and Effects is unchecked. If you don't, the stroke size might change when you use Transform Each. If this happens, just select all the shapes and change their Stroke width to 1 pt.
Note: The skill level of this tutorial is Easy. If you're unsure though, it's better to do the designs in order, because I explain things a bit less as we get further on.
With a 1 pt green stroke, make an Ellipse 150 pixels by 25 pixels.
Object > Transform > Transform Each, with Angle set to 30°. Click Copy (not OK).
Got to Object > Transform > Transform Again (or Command + D) four times to make the other copies. Then select all of the green ellipses and click Object > Group.
Now with a 1 pt blue stroke make an eight sided Star with an inner radius of 50 px and an outer radius of 75 px.
 
Using the Direct Selection Tool, select half of the anchor points. Use the Control Panel above to convert the anchor points to smooth. Then select the other half and convert them to smooth.
Note: an Illustrator oddity is that if you select all of the anchor points of an object, the Control Panel goes away. The Help file says: "To use the anchor point conversion options in the Control panel, only relevant anchor points, not the entire object, should be selected. If you select multiple objects, one of the objects must be only partially selected. When entire objects are selected, the Control panel options change to those that affect the entire object."
Use the Direct Selection Tool to select one of the outside anchor points. It might be a good idea to drag a box over the anchor point's location like this, rather than clicking it, to be sure you select the whole anchor point instead of one of its handles.
Grab the Rotate tool (R), then make the angle 180° and click OK.
Repeat this for each one of the outside anchor points individually. This can be done quickly if you leave the Rotate tool selected, hold Command to temporarily use the Direct Selection Tool to select the next anchor point, then hit enter to bring up the Rotate dialog box. Hit enter again to use the same values.
Now select all the inner anchor points. You can get them all at once by drawing a rectangle just so. Use the Scale tool to move them all a little outwards, which make the inside curves more rounded.
Then select one anchor point. Use the Scale Tool in the toolbox to enlarge it by 150%.
Repeat with all of the anchor points in the shape, inside and outside, one after another. Again, it won't take long if you leave the Scale tool selected, hold Command and select the anchor point, and then hit enter twice. When you're done it should look like this.
Select the whole object and use Object > Transform > Transform Each at 95% scale and -5% rotate.
Click Copy.

Hit Command + D twice to make two more copies. Then select all four shapes and Group them.
Select both groups and click Horizontal Align Center in the Control Panel (or the Align Panel), then Vertical Align Center as well.
With a 1 pt aqua stroke, make a square 100 px wide.
With the square selected, click Effect > Distort & Transform > Pucker & Bloat and make the effect 100%.
Go to Object > Expand Appearance. Then Object > Transform > Transform Each at 90% scale and -10% Rotation.
Command + D to make more copies. Then select them all and click Object > Group.
With a 1 pt red Stroke, make an ellipse 150 px by 25 px. Got to Object > Transform > Transform Each at 95% Scale and -8% Rotate.
Make several copies. Select all the red ovals, and Object > Group. Then Rotate the whole group 45°.
Select both groups and click Horizontal Align Center and then Vertical Align Center.
Use the Star tool to make a 7-point star with an outer radius of 75px. This will be a guide so the color doesn't matter.
I flipped mine so it points up, using Object > Transform > Reflect. Then go to Object > Lock > Selection to keep the guide star from moving. Set the stroke to 1 pt blue. Now, use the Pen tool to trace a 7-pointed star shape by clicking from one point to another as shown.
Got to Object > Unlock All, and delete the guide star. Use the Direct Selection Tool to select the anchors (half at a time, as we did in Design 1) and convert them to smooth.
Make a copy of the shape. Select one anchor point of the second star, and Scale it down to 50%. Repeat with all the anchor points.
Make a copy of the second star. Now there are three stars. On the third star, select one of the anchor points and use the Rotate tool to spin it 180°. Repeat this for all the anchor points.
Select all three stars and align their horizontal and vertical centers.
Change colors on two of the shapes, and to make it look more like an authentic Spirograph, scale the largest star down 90%.
Make an orange Square 100 px wide. Convert the anchor points to smooth.
Rotate each individual anchor point 180°.
Select the whole object, use Object > Transform > Rotate 10° and make eight copies.
Now select one of the shapes, Copy and then Paste in Front, and change its Stroke color to blue. With that shape still selected, Object > Transform > Transform Each at Scale 90% and Rotate -5°. Click Copy.
Use Command + D to make several copies.
Make a Star shape with eight points and an outer radius of 75 px. This star is going to be a guide. Use Object > Lock > Selection to keep it from moving.
Using the Pen tool with a 1 pt red Stroke, trace from point to point as shown below.
Go to Object > Unlock All and then delete the guide star.
Half at a time, convert the anchor points to smooth.
And one at a time, rotate them...
When they're all rotated it looks like the image below.
Using a 1 pt magenta Stroke, make a 4 pointed Star shape with outer radius of 75px.
Convert the anchor points to smooth. One at a time, rotate the four corner anchor points 180°.
Select the other four anchor points in the middle. Remove them using Object > Path > Remove Anchor Points. Copy the shape three times, Rotated at 22.5°.
Group the shapes, then select them along with the previous shape. Align vertically and horizontally.
With a 1 pt magenta Stroke, make a 100 px Circle.
Apply the Pucker & Bloat Effect at 140%.
Transform Each at 85% scale, -18° Rotation and click Copy. Then use Command + D to make three more copies.
Select the third largest copy, and go to Edit > Copy and then Edit > Paste in Front.
Change the Stroke to dark green, then Rotate by 36°.
In the Appearance Panel, double-click the Pucker and Bloat effect to edit it. Change the amount to 100%.
Now Transform Each at the previous settings as shown.
Variations
By now you can pretty much duplicate anything from the an Spirograph booklet.
Here's the green oval from Design 1, rotated and copied at a 5° angle, combined with a purple Ellipse 90 px by 60 px, rotated at a 20° angle.
This is the red Star from Design 3, its color changed to blue, with copies rotated -10° and scaled to 90%, combined with a 135px by 85px light blue Ellipse with copies rotated at 15 °.
This is the blue shape from Design 1, scaled down 90%, and the red shape from Design 5, copied and rotated 60°.
Here's two shapes from Design 3, the narrow one rotated -10° and scaled 90%, and the rounded one scaled down 80% then a copy at 80%.
Have fun! If you make something really cool with this, I would love to see what it looks like! Thanks!