A mathematical approach to advanced flower patterns

This has been brewing in my head for awhile. Its a way to pass time in Calculus and helps me understand - not only math - but flowers as well. I don't have much time to write as of right now but, think back to trig and polar graphs. I personally believe they flow so well with poi.

I'll write more soon but until then...

OH THE PATTERNS!

wow very complex patterns but one question why the repeats?

Actually I got bored in class and figured out how to make anti-spin petals (rose petals in graphing). How do you do pro-spin and those other funky ones?

Someone posted a spreadsheet that could generate these sorts of things for different arm-length/poi-length ratios, number of turns, and such a while ago.

If anyone is unable to find it, I can put it up somewhere.

How do you get the rose petals with 6, 10, 14, and any other number of petals that is even with an odd number as 1/2 of that number?

Practice.

Those are very cool concepts and all, but I think when actually executed, a lot of those patterns would be indistinguishable from each other. When doing poi, we don't see the whole pattern at the same time, so details like ones in the more intricate patterns on that sheet are diluted. And even when posing the move for a camera that could capture the whole pattern, they would require too precise hand movements to accurately repeat the entire trail.

That said, I don't really assume that you intended this as a practical approach to doing poi. This more or less just relates to theory of circles, which is a fun topic in and of itself, how ever conceptual it may be.

Sister, I mean with a graphing calculator lol. How would that certain amount of petals be so much harder than others. Because, well I can't type out all the symbols, so I'll type it out. For Sine of 3 theta, you would get 3 petals. For Sine of 2 Theta, you would get 4. Then Theta is multiplied by an odd number, you get that amount of petals, when you multiply it by and even number, you get twice the coefficient in petals. So certain amounts of petals confound me.

is there really a termn for drawing such "circles"?

Does here anyone is studying math and could get a term for having such patels with a calculator for example?

Try spirographs?

Hey guys, sorry for the late reply - I've been swamped with midterms. Anyways the main point of this post was to make people talk and it seemed to work!

So... yes not all of these patterns are possible and I feel any higher then 6 petals is pointless. Unless you're going really fast most viewers won't know the difference.(Well the 8 petal cateye flower does have a nice look to it). This is more of a conceptual post.

The patterns with 6, 10 or 14 petals are simple. Either r=cos theta and r=sin theta or r=cos (theta - Pi/2).

Recently I've found a way to trace out a pentagram using polar coordinates! I have to go to class, so I'll post pictures tonite.

I didn't found the actual post ... but below are miscellanies which enable to vizualise the effect of the "modulus" part on a given "harmonic" part of a pattern.

If you wonder what i mean by "harmonic" and "modulus" parts or want to know what my definition of a pattern is ... take a look here at first -> Explanation

These patterns have been traced on Excel ... with the help of a mathematical description :



The "modulus" part range ... i.e. the ratio PoïLength/Arm Length ... is successively 1,4/5,3/4,2/3,3/5,1/2,2/5,1/3,1/4,1/5 for each patterns.

The first : patterns with a 1 # "harmonic" part ... with # from 1 to 7.
The second : patterns with a 1 -# "harmonic" part ... with # from 1 to 7.
The third : a few 3 # & 3 -# "harmonic" part patterns.
And so on.

The concentric little circles pattern below have a 0 1 "harmonic" part.
The concentric big circles pattern below have a 1 0 "harmonic" part.