A rose is just a rose?

One of the simplest shapes to be created by math is the so-called “rose curve”, well documented in this Wikipedia page. It’s created by a simple set of equations:

image13A(smaller)

(hate the stupid WordPress scaling, blurs my images) but anyway here’s what the first few look like (k = 1…9):

image13B

Pretty boring, huh, so let’s see if we can kick it up a notch.

First, let’s experiment with non-integer k.

image13C

Not only does this create more “petals” but it also overlaps them in the interior in interesting ways.

So let’s try making the r have multiple harmonics:

image13D

4/5 sin(4t) + 1/5 sin(7t): A bit more interesting.

image13E

4/5 sin(3t) + 1/4 sin(3.5t) + 1/10 sin(6t), or perhaps

image13F

4/5 sin(4t) + 1/5 sin (3-1/3t) + 1/10 sin(3-2/3t)

And we could go on but it might take a while to find something very different, hence the need for RSE (Rapid Shape Experimentation) as mentioned in previous post.

Or what about taking r to some power?

image13G

But let’s also try superimposing some.

image13H

And with different petal lengths

image13I

or more symmetrically changing petal lengths

image13J

or multiple symmetries combined

image13K

Can you tell which values of k I used?

Or multiple symmetries with different petal lengths?

image13L

Now this should give a flavor of how a rather simple parametric equation can be permuted into a variety of shapes. None of them, however, to my eye even begin to look like a “rose” so I’m not quite sure how this function got named. Even more experimentation than I’ve shown in this post can be done and at some point some interesting shapes are going to be found, just a matter of how patient you are and creative at tweaking tieflume code to generate lots of variations.

So I’ll leave you with this one, you figure out what generated it (and how to make it better).

image13M

So stay tuned

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About dmill96

old fat (but now getting trim and fit) guy, who used to create software in Silicon Valley (almost before it was called that), who used to go backpacking and bicycling and cross-country skiing and now geodashes, drives AWD in Wyoming, takes pictures, and writes long blog posts and does xizquvjyk.
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