Script for rendering Taylor series whose inverses equal their derivatives.
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wan-may 1fb4bcf0fe
readme, fixup
5 months ago
ansatz.lua Large commit, fixed large mistake in calculating Ansatz values, added tests for FDB series plot. 1 year ago
diff.lua Feverish insensate spurt: 1 year ago
fdb.lua readme, fixup 5 months ago
interpolant.lua Large commit, fixed large mistake in calculating Ansatz values, added tests for FDB series plot. 1 year ago
main.lua readme, fixup 5 months ago
readme.txt readme, fixup 5 months ago

readme.txt

Bespoke script for calculating and plotting some series solutions

of the functional equation f'( f( x ) ) = x.

Idea: suppose f has fixed point p,
apply the chain rule to functional equation
get values of f's derivatives at p
get truncated taylor series expansion of f at p,
plot series to get some idea about values, convergence.

We use Faa Di Bruno's formula for iterated derivatives, in terms of Bell numbers.
We also plot the "ansatz" solution, i.e. the solution of the form x -> a * x ^ b where a and b are positive.

Uses LOVE as a dependency for its plotting: https://love2d.org
Solution is plotted in red, first derivative is plotted in green.

Keys:
Q - Increase p
E - Decrease p
WASD - Translate view
Z - Zoom in
C - Zoom out
F - Increase order of series expansion
R - Decrease order