24 lines
795 B
Plaintext
24 lines
795 B
Plaintext
Bespoke script for calculating and plotting some series solutions
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of the functional equation f'( f( x ) ) = x.
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Idea: suppose f has fixed point p,
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apply the chain rule to functional equation
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get values of f's derivatives at p
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get truncated taylor series expansion of f at p,
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plot series to get some idea about values, convergence.
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We use Faa Di Bruno's formula for iterated derivatives, in terms of Bell numbers.
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We also plot the "ansatz" solution, i.e. the solution of the form x -> a * x ^ b where a and b are positive.
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Uses LOVE as a dependency for its plotting: https://love2d.org
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Solution is plotted in red, first derivative is plotted in green.
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Keys:
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Q - Increase p
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E - Decrease p
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WASD - Translate view
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Z - Zoom in
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C - Zoom out
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F - Increase order of series expansion
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R - Decrease order
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