new fatou.gp program

[Ember Edison]

I updated the main fatou.gp code to include the more resilient matrix version from Ember's post.  But matrix_ir doesn't know how many theta sample points to use and defaults to 18 theta samples   sexpinit(B) is still the suggested version to use for generic real and complex bases, which loops, increasing precision at each iteration instead of using the matrix version of the same solution family.  So if you have a base that gives errors or for sexpinit(B) ....
matrix_ir(B,lctr,ltht,myctr,myir); /* B is now the tetration base, instead of the internally used k=log(log(B))+1 */
lctr is the number of sample points in the slog Taylor series
ltht is the number of sample points in the theta mapping; defaults to 18
myctr is sampling radius ratio.
myir is the inner radius radio with respect to the sampling radius ratio
matrix_ir(exp(1)); /* automatic settings work well for many real valued bases to give >32 digits of precision */
matrix_ir(31825+3345*I,400,,8/9); /* 400 samples, myctr=8/9 for convergence; 29 digits  */
Here are some settings for other crazy bases like base=0.15, or base=0.1, or base 0.2*I ....
matrix_ir(0.2*I,400,90,14/15,45/46); /* 20 decimal digits of precision */
matrix_ir(0.15,400,90,14/15,45/46); /* 16.5 decimal digits of precision */
matrix_ir(0.1+I*1E-30,400,250,14/15,45/46); /* 16 decimal digits of precision */

Sorry, but please test it:

Code:

matrix_ir(1E6,,,19/20);circchart("1E6.csv")

   

Code:

hexinit(1.6);[ipent(3),ihex(2)]
hexinit(1.7);[pent(8),ihex(3)]
hexinit(22);hex(2)
pentinit(3381);pent(2)
matrix_ir(1E9,,,19/20);sexp(1)