Directory Contents
==================
Presented in historical order.

../generate: pre 2010
   -- All the 2D work prior to the 2010 refactoring is in this
      directory, including the fractals, the ordinary generating
      functions of the number-theoretic functions, etc.

misc: 2000-2010
   -- Misc junk
      fibonacci-farey.pl: 27 Dec 2000 limit of the mandelbrot set
      prime.pl: 24 March 2001
      prime.scm: 29 June 2004
      thue-morse-farey.pl: 12 Oct 2004 limit of the mandelbrot set
      prime-bit.pl: 7 may 2010

driebe: 19 June 2001
   -- Dean Driebe teaches me what the frobenius-perron operator is,
      and shows me how to solve it for the Bernoulli Map. Very first
      forays into what becomes an exploration of modular symetries.

      bern-coherent.pl: 19 June 2001 Coherent eigenstates of
                  frobenius-perron operator of bernoulli map.
      legendre.scm: 17 July 2001 Compute Driebes eqn (A.33) integral
                                 of rescaled legendre's
      div.C: 19 July 2001 foolin around

stern-gerlach: 9 July 2001, 19 May 2002
   -- Simulate classical magnetic dipole absorbing soft photon impulses.
      Simulate classical magnetic dipole in stern gerlach magnet.

hyperconverge: 11 October 2001
   -- simple hyperconvergent series -- Euler's series
      (exponential integral) abramowitz & stegun eqn 5.1.51

billiards: November 2001
   -- Ray tracing of Sinai's Billiards. Traces both classical-mechanics
      rays, and also path integral, for exploring diffraction.

      mfp: 18 March 2002 Mean free path in the billiards

chiral-bag: 4 July 2003
   -- Chiral Bag eigenfunctions. From my PhD thesis.
      Originally written in FORTRAN in 1983. Ported to C in July 2003.

queue: 3 Sept 2003
   -- The classic 3n+1 if odd else n/2 if even problem.

continued-frobenius: Dec 2003 to 2010
   -- Frobenius Peron operator for continued fractions.
      This is the Frobenius-Perron operator that Driebe taught me about,
      but now applied to continued fractions, instead of the Bernoulli shift.

      integ.c: Dec 5 2003
      diverge.c: Dec 7 2003
      cubic.c: Dec 8 2003
      valuate.c: Dec 14 2003
      gsl-diag.c: Dec 18 2003
      mathcheck.c: Dec 23 2003
      bern.c: Dec 28 2003
      riemann.c: Dec 28 2003
      sin.c: Dec 29 2003
      zero.c: Dec 29 2003
      tryall.c: Jan 6 2004
      gsl-eigen.c: Jan 6 2004
      det.c: Jan 6 2004
      frobenius.c: Jan 10 2004
      eicheck.c: Jan 11 2004
      eig.c: Jan 12 2004
      stieltjes.c: Sep 24 2004
      beta.c: Nov 27 2004
      bern_h.c: Dec 2 2004
      alpha.c: Dec 8 2004
      zeta-sum.c: Dec 16 2004
      zeta-zero.c: Dec 18 2004
      zyx.c: Dec 18 2004
      character.c: Dec 24 2004
      zeta-takagi.c: Jan 27 2005
      sum.c: Feb 13 2005
      eta.c: Feb 13 2005
      swap.c: Feb 26 2005
      binom-graph.c: Jun 29 2005
      harmonic.c: Aug 28 2005
      zetafn.c: Dec 18 2005
      stirling.c: May 29 2006
      ache.c: Jul 3 2007
      asubn.c: Jul 3 2007
      rational-sum.c: Jun 1 2008
      eigen.c: Jan 11 2010
      diagon.c: Jan 11 2010
      normal.c: Jan 11 2010
      quest.c: Feb 18 2010

farey: February 2004-2007
   -- Farey fractions. Haven't yet realized connection between Farey
      fractions and continued fractions. This is explored here.

      prt-farey.C: February 2004 print Farey fractions
      density.C: 2 February 2004 Lengths of continued fractions
      trinary.c: 12 October 2004 3-adic type continued fraction
      binom.c: 25 August 2006 Experiments with binomial coefficients
      st-xform.C: 21 March 2007 Some xform of continued fractions
      divisor-rep.C: January 2011 divisors and continued fractions

modular: 4 November 2004
   -- orbit of vector under 3D representation of modular group.

free-group: 24 December 2004
   -- Freely generated Group games

gap: late 2004, early 2005
   -- Extensive exploration of continued fractions, Takagi curve,
      orbits, p-adic numbers, hyperbolic rotations, Bernoulli operator,
      Levy dragons.

      This is where I slowly come to realize that the symmetries of
      assorted dyadic fractals, continued fractions, binary trees, etc.
      are the symmetries of SL(2,Z) the modular group, or rather, the
      modular monoid. So the source code does not yet call it that,
      because I hadn't yet made that realization.

      c-takagi.c: October 2004 Takagi curve for complex-valued w
      gappy.C: October 2004 Games with Gaps
      sway.C: October 2004 swaying of the continued fraction expansion
      feigen.C: October 2004 Bernoulli-map eigenfns concated with Minkowski map
      ising.C: October 2004 Ising model inspired takagi curve.
      summy.C: October 2004 Wacky sums of the GKW operator
      sym-fun.C: October 2004 Sawtooth and related functions generated by
                              the Minkowski symmetery group
      entropy.C: October 2004 Shannon entropy of continued fractions
      takagi.C: October 2004 Draw the Takagi curve
      sum.c: 25 October 2004 junk
      dyadic.C: November 2004 Polynomials generated from binary expansion.
      orbit.C: November 2004 Orbits of vectors under the dyadic representation
                             of the modular group.
      conj.c: 9 Dec 2004 Conjugate map explorer of the tent map
      measure.c: 25 October 2008 *discontinuous* eigenfunctions of the
                                 Bernoulli operator. product topology.

      cantor-dist.C: Oct 2004 fractal measure of Cantor polynomial function
      simplicity.C: Oct 19 2004 junk
      exacto.C: Oct 20 2004 Exact relations on continued fractions
      padic.C: Oct 21 2004 p-adic number games
      sym-pow.C: Oct 22 2004 Symmetry of the Minkowski symmetry group.
      sym.C: Oct 23 2004 Explore symmetries of continued fractions
      fiddle.C: Oct 26 2004 misc fiddling
      theta.C: Oct 30 2004 Line segmments of the hyperbolic curves
      tree.C: Oct 31 2004 eigenfunctions of Bernoulli operator.
                           proto-forms of the Levy Dragons
      fliptree.C: Nov 3 2004 show tree for 1 to infinity
      pair.C: November 2004 Final pair of continue fraction
      mute.C: Nov 3 2004 Integrals of permutated, swapped continued fractions.
      gkw.C: Nov 13 2004 Explore gauss-kuzmin-wirsing symmetries.
      zeta.C: Dec 4 2004 Explore Hurwitz zeta eigenfunctions of Bernoulli map
      orbit-s.C: Dec 7 2004 Orbits of vectors under the dyadic representation
                            of the modular group.
      moebius.C: Dec 14 2004 Moebius transform of the Takagi curve
      rand-measure.C: Jan 9 2005 Distribution of the random numbers
                                 aka multi-fractal measures.
      mod.C: Feb 19 2005 Explore limits of modular functions.
      pegs.C: Mar 15 2005 Measure the distance to the nearest peg in a grid.
      tent-map.C: Jul 4 2005 Dyadic symbolic values of the tent map.
      quest.C: Oct 9 2005 Draw the Question mark
      takagi-n.C: December 2005 Non-dyadic variant of the Takagi curve.
      vanish.C: Feb 18 2007 Functions that vanish on binary numbers.

fdist: late 2004-2010
   -- Distribution of the Farey Numbers on the unit interval.
      At this point, I had not yet realized the connection between the
      Farey numbers and the Minkowski Questin Mark, so am discovering it
      here.

      rdist.C: October 2004 Distribution of rationals. GnuGMP version.
      fdist.C: October 2004 Distribution of the Farey Numbers
      jdist.C: October 2004 variation on above.
      fourier.C: October 2004 Fourier transform of Distribution of the
                              Farey Numbers
      fanal.C, janal.C: October 2004 varations on above.
      f-wavelet.C: October 2004 Binary coefficieints of Distribution of
                                the Farey Numbers. Wavelet style.
      hardy.C: October 2004 Poison integral of the Minkowski measure
                            ("singular inner function" in the theory
                            of Hardy spaces.)
      ftag.C: 4 September 2008 Farey dist as a Cantor set, using log of
                               Takagi. Use a Stupa energy potential,
                               compare Kac potential.
      shift.C: 4 September 2008 Binary shift of continued fractions.
      takagi-dist.C: October 2008 Takagi-style distribution.
      akk.C: 3 Oct 2008 Utility to graph the a_k
      mink-meas.C: 8 October 2008 Minkowski Measure explicit construction.
      two-d.C: 14 March 2010 Two-dimensional rep of dyadic group.
                             Verify eigenvalues of dyadic GKW.
      qdiff.C: 15 March 2010 Experimental diffs
      decomp.C: 23 March 2010 Linear decomposition of continuous &
                              differentiable eigenvalues into fractals.
      taulim.C: 23 March 2010 Limiting behaviour of the GKW eigenfuncs at zero.

ising: late 2004-2006
   -- Explore modular relationship of 1D Ising and Kac models.
      takagi-gral.c: October 2004 integrals of the Takagi curve
      ising.c: 25 Sept 2005 One-dimensional Ising model and Kac model
                            state of the system is encoded as 2-adic string.
      kac.c: 25 Sept 2005 Kac model with cylinder-set topology
      lr-tree.c: 16 Sept 2006 Encode binary LR trees as dyadic fractions
      partition.c: 18 Sept 2006 the q-series-like partition function

num-theory: late 2004-2010
   -- Graphs of slices of ordinary generating funcs of number-theoretic
      functions, with an attempt to relate to minkowski-like behavior.

      ndist.c: 29 Dec 2004 graph of totient of dyadics on unit interval
      buddy.c: 26 May 2005 spectral analysis of interior of Mandelbrot set
      angular.c: 30 May 2005 circular slice totient and other number-theoretic
      hyperg.c: 20 June 2005 hypergeometric series
      mertens.c: 11 July 2006 graph of Mertens function.
      series.c: 13 July 2006 maclaurin series of num-theo funcs.
      divisor.c: 12 Sept 2006 series involving divisor function.
      liouville.c: 4 June 2007 series involving Liouville function
      von_mangoldt.c: 4 June 2007 Chebyshev (sum of von Mangoldt) function
      interval.c: 19 Aug 2009 num-theo funcs after reversing bit order
      cat-algebra.c: 28 Nov 2010 Categorical algebra mobius to num-theo mobius
      fourier.C: 28 Nov 2010 Fourier xforms of num-theo funcs after
                             similarity xform by question mark.

symbolic: 17 Jan 2005
   -- Hacky code to compute metric tensors, Christoffel symbols,
      Ricci tensor, Scalar curvature. Written because I'm too
      lazy to learn real computer algebra systems.

de-rham: 14 May 2005
   -- Draw deRham curves with different algos.
      affine.c: 14 May 2005 Draw deRham curves by iteration of affine matrices.
      curve.C: 14 May 2005 ... by iteration of functions.
      de-rham.c: 14 May 2005 ... by iteration of functions.

surface: 12 Jun 2005
   -- Graphs of the lengths and energies of geodesics on the Riemann
      surface/fundamental domain.

weyl: 14 July 2005
   -- Weyl group functions hack

green: 18 Dec 2005
   -- Green functions for the Bernoulli process
      polynomial.c: 16 December 2005 Semi-Symbolic polynomial handling
      green.c: 18 Dec 2005 Green functions for the Bernoulli process
      sho.c: November 2006 hyperbolic simple harmonic oscillator eigenvalues

wavelet: 3 January 2006
   -- matrix elements of the transfer operator (composition operator)
      of the Minkowski question mark function. The basis are Haar wavelets.

hyperbolic: January 2006, 2007
   -- build the question mark function from hyperbolic roations.
      Assorted hyperbolic plane (Poincare disk) drawing utils & etc.
      rotations.c: January 2006 Try to build the question mark function
                                out of hyperbolic roations.
      eps.c: April 2007 Encapsulated PostScript utilities
      flt-eps.c: April 2007 Fractional linear transfor (flt) postscript drawing
      mod-tree.c: April 2007 Binary tree on the hyperbolic upper half-plane
                             (or on poincare disk)
                             Built algebraically from modular xforms
                             as opposed to the geometric construction in tree.c
      similar.c: April 2007 Draw a binary tree on the poincare disk
      tree.c: April 2007 Draw a binary tree on the hyperbolic disk,
                         using postscript. Explictly geometric construction.
      perimeter.c: 7 May 2007 Map tree to perimeter of the circle.
      feig.c: 15 August 2016 Feignbaum ratios in the forking of the tree.

schroedinger: 24 January 2006
   -- solutions to misc 1-D schroedinger equations, Galois inspired.

norlund-rice: 19 Feb 2006
   -- baez.c: 22 Feb 2006 Baez-Duarte sum
   -- dsubn-analytic.c: 13 Nov 2006 Analytic fit to d_n
   -- zeta-imag.c: 19 Feb 2006 Graph of Riemann zeta on the critical line

bignum: 2006-2015
   -- Gnu GMP bignum (arbitrary precistion) implementation of a large
      variety of assorted number-theoretic and analytic-combinatoric
      functions. This is eventually cleaned up and nicely organized as
      the Anant library.

plouffe: 13 May 2006
   -- Explore some of the sums given by Simon Plouffe.
      Specifically, the modular-like sums involving 1/1+exp(2pi n)

hurwitz: October 2006
   -- Hurwitz zeta function for arbitrary complex argument.
      Polylogarithm for arbitrary complex argument.
      This is part of a complete study of the polylog, that resulted
      in the publication of the polylog paper.
      hurwitz.c: October 2006  Hurwitz zeta function for complex argument
      polylog.c: November 2006 Borwein-style polylogarithm.
      check.cc: 30 Nov 2014 Quick double-check

polyhedra: 28 February 2007
   -- Map a binary tree onto a polyhedron.
      More or less equivalent to a Markov chain.

presentation: 16 March 2007
   -- Brute force search for group presentations. Includes braid group.
      Heisenberg group, various polylog groups. Used to verify the
      monodromy of the polylogarithm. This was used to confirm ideas
      regarding the polylogarithm, which were eventually published in
      the polylog paper.

entropy: 1 June 2008
   -- Entropy of Gauss-Kuzmin, entropy of rationals.
      gauss-kuzmin.c: 1 June 2008 Gauss-Kuzmin entropy
      defacto.C: 2 June 2008 Explore the defacto entropy of rational numbers.
      entropy.C: 2 June 2008 Entropy of individual expansions of rationals.

fourier-question: 20 June 2008
   -- Eigenvalues & eigenvectors of Fourier of Minkowski-question operator
      eigen.c: Sept 2004 Eigenvalue and eigenvector finding w/LAPACK
      eigen-extrap.c: 20 June 2008 eigenvalues of the Fourier of
                                   Minkowski-question operator
      gral-explore.c: 20 June 2008 matrix elements of fourier of
                                   minkowski question mark
      gral-matrix.c: 19 June 2008 brute force matrix elements
      gral-simple.c: 20 June 2008 brute force matrix elements
      counting.c: 12 Feb 2010 quick-n-dirty prime-couting attempt.
                              Fantiastic results!

fredholm: 2 September 2008
   -- Green functions, propagators, etc. for articifically constructed
      things from the Riemnann zeta. Seems to be a failure, no insight gained.

zipf: 15 March 2009
   -- Experiments with random strings

walsh: July 2009
   -- Walsh functions provide a basis for square-integrable functions.
      The 'prime factors' of the walsh functions are the Rademacher functions.
      Derivative of minkowski-question-mark, integrated with
      the Walsh functions
      Fractal eigenfunctions of GKW. (Jan 2016)

gkw: 10 January 2010
   -- Newer Gauss-Kuzmin-Wirsing stuff
      Oroginal, older GKW stuff is in the continued-frobenius directory
      hurwitz.c: 10 January 2010 graph of hurwitz zeta
      asymptote.c: 21 Jan 2010 Find saddle point of asymptotic expansion
      diag.c: 23 Jan 2010 check saddle point
      similar.c: 21 Feb 2010 similarity -conjugacy

synthetic: Nov 2010
   -- Some intractable sum over Riemann zeta. Dead end.

yarh: Dec 2010
   -- "Yet Another Riemann Hypothesis", Looks at zeros in the critical
      strip obtained by integrating permutations of continued fractions.
      Inspired by noticing that Riemann zeta is integral of truncated
      continued fraction.

julia: 27 December 2011
   -- Julia set explorer for the Mandelbrot bulb.
      assign a string of L,R values to each point in the Julia set

geodesic: 30 August 2012
   -- Explores the symbol dynamics of the SL(2,Z) fundamental domain.
      Explore geodesics on the fundamental domain of the modular group
      by ray-tracing.  Arbitrary-precision version.
      Explore Ornstein isomorphism theorem and the Cantor set.

fractions: 20 March 2013
   -- Accumulating fractions into bins by bin-counting.
      A regular fractal pattern emerges, similar to many others.
      Never got around to relating it to earlier results.

holomorphic-sho: 30 November 2013
   -- Some failed attempt at holomorphic simple harmonic oscillator.

alternate: 1 June 2014
   -- Alternating sums inspired by differential operators. Both applied
      for binary expansions and to continued frac expansions.

graph: 23 November 2014
   -- Schroedinger wave function for Number-Theoretic functions
      Solves 1D Schroedinger eqn on a lattice, where the potential
      is given by assorted number-theoretic functions.

      bessy.cc: 23 Nov 2014 Schroedinger eqn in a 1D lattice.
                            Graph the bessel-function-like solutions.
      eigenwave.cc: 23 Nov 2014 Schroedinger eqn in a 1D lattice.
                                Plot the wave function itself.
      potential.cc: 23 Nov 2014 Sanity check some numer-theoretic functions
      schroed.cc: 23 Nov 2014 Schroedinger eqn in a 1D lattice.
                              Focus on number-theoretic potentials.
      eigenzee.cc: 27 Nov 2014 Graph of eigenvalues of disvisor function

divisor: 30 November 2014
   -- Compute the divisor operator and the mobius operator.
      Verify that each is the left-right inverse of the other.
      Verify the totient function.

ffbasis: 25 December 2014
   -- Falling factorial basis for divisor/multiplicative functions

calkin-wilf: 19 Sept 2015
   -- A recursive function that gives the denominator of the
      Stern-Brocot tree. Graphing it, its reminiscent of Minkowski
      measure.
      The fusc function gives the denominators of the stern-brocot tree.
      Graphing the denominators-only gives a blanc-mange-like function.
      The relation to the question mark function, if any, remains a
      mystery.

frontal: 7 Sept 2015
   -- Explore the analytic continuation described in frontal.lyx

pompeiu: 19 Sept 2015
   -- Graph of one very specific Pompieu function, just for grins.

measure: 21 September 2015
   -- (exact) approximation and bound for the Minkowski measure,
      inclusing scaling of the thing.

sum: 29 August 2015
   -- Sums of binary digits. Forms fratals in 1D, 2D.

lattice: 27 September 2015
   -- Graph every line of the form (ax+b)/(cx+d) for SL(2,Z)
      The resulting pictures are beautiful!

clifford: 28 April 2016
   -- Basis of Clifford algebra has a non-canonical mapping to binary tree.
      Multiplication in the Clifford algebra induces multiplication of
      such trees. What does this look like (when mapped to bit-strings?)

similar: 29 Sept 2016
   -- When is a Mobius xform  (ax+b)/(cx+d) similar to 1/x ?

gpf: April, Oct 2016
   -- Greatest Prime factor, exponential generating function.

arithmexpic: Oct 2016
   -- Exponential generating function for the number-theoretic
      functions. Vast numbers of very pretty pictures.

logpf: 30 June 2017
   -- Continuing in the vein of GPF, arithmexpic, but for logarithms.

snake: 27 Nov 2017
   -- Look at the pseudo-arc as defined by WAYNE LEWIS AND PIOTR MINC
      DRAWING THE PSEUDO-ARC  Very little done here.

circle: 4 Dec 2017
   -- Recreate some of the old circle-map stuff. Add in simplifications.
      Lots of very pretty images!

beta-xform: Dec 2017 through 2020
   -- Look at simplifications of Bernoulli map. Look at the Beta
      Transform. Lots and lots of pretty pictures!
      The Beta Transform is the iterated eqn (bx mod 1) for
      for 1<b<2. See the README for details.

adammaj1: Dec 2017
   -- code from Adam Majewski which he wanted me to look at & fix.

borel-mink: 31 January 2018
   -- Look at the Borel transform of the Minkowski fn.
      Also the Riesz–Herglotz transform.

mobexpic: 17 January 2019
   -- Like arithmexpic, but a deeper look into Mobius and iterated units.

redheffer: 9 February 2019
   -- The Redheffer operator, which has any/every completely
      multiplicative series as an eigenvector.

yarh-two: Feb 2019
   -- Another Riemann Hypothesis about multiplicative series.

scatter: 11 July 2019
   -- generic scatterplot tool

dynamical-zeta: 10 Sept 2020
   -- The dynamical zeta sum_n n^-s exp (2pi ix_n) for sequences x_n.

odometer: 13 September 2020
   -- Bernoulli and Ornstein odometers

beta-expand: September-October 2020
   -- Beta expansions. Described in the paper beta-expand.lyx.
      The Beta Transform is the iterated eqn (bx mod 1) for
      for 1<b<2. See the README for details.

polylog: October 2023
   -- See also hurwitz, above, where the old main polylog work happened.
      This directory contains all the scripting and new work,
      used to make more polylog movies.

circle-metric: November 2023
   -- Revisit the old circle-map stuff. Extend, expand, look at more
      things. Originally meant to explore the idea of series metrics,
      but blew up into a more general exploration.

markov: December 2023
   -- Markov numbers

mandelbrot: December 2023
   -- Yet another mandelbrot explorer. Examines rate of convergence inside
      the Mandelbrot set.

The End.
--------
That's all, folks!