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 [hidden email] http://mail.python.org/mailman/listinfo/edu-sig superformula.py (7K) Download Attachment |
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 > [hidden email] > 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. _______________________________________________ Edu-sig mailing list [hidden email] http://mail.python.org/mailman/listinfo/edu-sig |
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