So first, follow the instructions in David's NINA article to make a spirograph. I played around with the settings a bit until I got something that resembled a flower.
Then I copied and pasted my NINA Script flower into Illustrator. I wanted to color the flower in shades of pink and red, in honor of Valentine's Day, so I loaded up Illustrator's built-in Flower color swatches: Peony, Pink Rose, and Red Rose.
Using the Live Paint Bucket tool, I gave my flower some colors. If you've never used the Live Paint Bucket tool, you should give it a try. Here is a great article on the Live Paint Bucket tool.
In case you're not familiar with the Live Paint Bucket tool, and you've ever gotten an Illustrator file from another designer and seen these unusual corner handles, these are corner handles for a Live Paint Group.
Here is my flower as I had completed my coloring of it.
To give it a more organic, less mathematical feel, I twirled it a bit. Want to learn more about the twirl tool? Read this article.
Happy Valentine's Day!