There are a great many such parametric formulae, such as

hypergeometric sequences and their sums. You can get very interesting

results by plotting the roots of a polynomial as the coefficients

vary, without ever letting two roots coincide. It is possible to

generate all knots and links in this way, by letting the graph wrap

around.

Given

* A parameter t in the range [0,1]

* A polynomial P = Σaᵢxⁱ for i in the range from 0 to n

* Continuous but not necessarily differentiable complex-valued

functions aᵢ(t), with aᵢ(0) = aᵢ(1)

for which P has no repeated roots at any value of t, we can take the

graphs of the n complex roots of P for each t, graph them in three

dimensions, and then topologically wrap the whole thing around into a

donut, joining t = 0 and t = 1, where the roots are the same, but may

be permuted.

The following diagram must be viewed in a monospace font in order to make sense.

_______ _____

\/

_______/\_____

On Sat, May 21, 2011 at 17:11, Gregor Lingl <

[hidden email]> wrote:

> Hi all,

>

> recently I stumbled (once more) over a posting by our friend

> Daniel Ajoy about the superformula (I think it was in a Logo-Forum):

>

>

http://en.wikipedia.org/wiki/Superformula>

> On the other side Kirby wrote interesting suggestions

> about using generators.

>

> Now, weekend, bad weather, some sparetime, I

> assembled an implementation of a superformula-viewer

> using pygame. It runs with Python 2.6 or higher, also

> 3.x, of course

>

> You'll find it here for download:

>

>

http://dl.dropbox.com/u/2016850/superformula.py>

> or appended (which sometimes / for some of you)

> doesn't work well depending on the browser or whatever.

>

> The script uses generators for generating the pointlists

> of the graph of the superformula and also for generating

> colors for the segments of the graph-area.

>

> Morover I've prepared a q&d slider class, which possibly

> doesn't use the canonical way of processing events in

> pygame but works fine for this application.

>

> Critical comments and feedback and also questions, of course,

> are welcome.

>

> Perhaps someone is willing to amend the docstrings,

> which suffer from my clumsy English and could well

> be more clear.

>

> Amendments of the code, espercially ones, which make it

> more readable and easier to understand, also.

>

> Useful for classroom use? Perhaps to difficult?

>

> Best regards,

> Gregor

>

>

>

> _______________________________________________

> Edu-sig mailing list

>

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>

http://mail.python.org/mailman/listinfo/edu-sig>

>

--

Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin

Silent Thunder is my name, and Children are my nation.

The Cosmos is my dwelling place, the Truth my destination.

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