Right - Basically I've made a spreadsheet in which you can enter values for a few variables such as arm/poi lengths/directions, and number of spins, and it will draw a few graphs of the trails left by poi doing compound circles. I know there's already a lot on here about flowers, so I haven't gone into any detail about how to do them. I also know people have posted pictures of a few different types of flower, but thought it would be good if you could change all the variables yourself. Here are a few threads that it may be worth looking at as well if you want to get full use out of it:
http://www.homeofpoi.com/ubbthreads/showflat.php/Cat/0/Number/629752 has some nice pictures and explanations.
http://www.homeofpoi.com/ubbthreads/showflat.php/Cat/0/Number/335783 has some nice ideas that you can model with the spreadsheet.
http://www.homeofpoi.com/ubbthreads/showflat.php/Cat/0/Number/363078. As does this one.
http://www.homeofpoi.com/ubbthreads/showflat.php/Cat/0/Number/371218. This one tells you about how to actually do flowers.
It's a bit limited at the moment. Firstly you need excel to open it. I don't know much about computers so I don't know how to turn it into a web page or make it as a stand alone program. If anyone does let me know and I'll try and do it.
Also I'd like to be able to animate it. Not sure how to do that either.
It's also limited with regards to the type of compound circles it can model. For a start, they're all in one plane, and they don't change direction mid pattern. There's lots of nice patterns that involve changing direction. This model doesn't do that. It just does one rotation of each arm in the direction(s) you specify. It also only models arms/poi going at a constant speed - So it doesn't do lockouts or anything like that. Still, if you play around, there are countless possibilities even with these few variables. Before i made this i never really considered the different patterns made by changing your poi length - It actually makes a remarkable difference. You'll soon start to see that flowers are only a special type of compound circle, and that lots of other patterns that look nothing like flowers are possible.
Anyway here's the link:
http://users.ox.ac.uk/~wadh2520/Compund%20Circles.xls
There's probably a few bugs, if you spot them let me know. Also general comments would be appreciated, especially ways to improve it. Also if you find interesting patterns, let me know, or maybe post a picture of them on here, with the values you need to make it.
have fun