Hubbard and Papadantonakis.  The first loop whose associated monodromy
automorphism is convincing.

The following tables give the permutation on the critical points down to depth 10;
the labelling is by itinerary.

Generated using SaddleDrop 0.5.3


Level 9

A
0.111001000 0.101001000  *
0.111001001 0.101001001  *
0.111001011 0.101001011  *
0.111001010 0.101001010  *
0.111001110 0.101001110  *
0.111001111 0.101001111  *
0.111001101 0.101001101  *
0.111001100 0.101001100  *
0.111000100 0.101000100  *
0.111000101 0.101000101  *
0.111000111 0.101000111  *
0.111000110 0.101000110  *
0.111000010 0.101000010  *
0.111000011 0.101000011  *
0.111000001 0.101000001  *
0.111000000 0.101000000  *
0.101000000 0.111000000  *
0.101000001 0.111000001  *
0.101000011 0.111000011  *
0.101000010 0.111000010  *
0.101000110 0.111000110  *
0.101000111 0.111000111  *
0.101000101 0.111000101  *
0.101000100 0.111000100  *
0.101001100 0.111001100  *
0.101001101 0.111001101  *
0.101001111 0.111001111  *
0.101001110 0.111001110  *
0.101001010 0.111001010  *
0.101001011 0.111001011  *
0.101001001 0.111001001  *
0.101001000 0.111001000  *


B
0.011100100 0.010100100  *
0.011100101 0.010100101  *
0.011100111 0.010100111  *
0.011100110 0.010100110  *
0.011100010 0.010100010  *
0.011100011 0.010100011  *
0.011100001 0.010100001  *
0.011100000 0.010100000  *
0.010100000 0.011100000  *
0.010100001 0.011100001  *
0.010100011 0.011100011  *
0.010100010 0.011100010  *
0.010100110 0.011100110  *
0.010100111 0.011100111  *
0.010100101 0.011100101  *
0.010100100 0.011100100  *

C
0.001110010 0.001010010  *
0.001110011 0.001010011  *
0.001110001 0.001010001  *
0.001110000 0.001010000  *
0.001010000 0.001110000  *
0.001010001 0.001110001  *
0.001010011 0.001110011  *
0.001010010 0.001110010  *

D
0.000111001 0.000101001  *
0.000111000 0.000101000  *
0.000101000 0.000111000  *
0.000101001 0.000111001  *
0.100101001 0.100111001  *
0.100101000 0.100111000  *
0.100111000 0.100101000  *
0.100111001 0.100101001  *

E
0.000011100 0.000010100  *
0.000010100 0.000011100  *
0.010010100 0.010011100  *
0.010011100 0.010010100  *
0.110011100 0.110010100  *
0.110010100 0.110011100  *
0.100010100 0.100011100  *
0.100011100 0.100010100  *




A	00.1x100hhhh	16	x2
B	0.01x100hhh	8	x2
C	0.001x100hh	4	x2
D	0.h001x100h	4	x2
E	0.hh001x100	4	x2






Level 10:

A
0.1110010000 0.1010010000 *
0.1110010001 0.1010010001 *
0.1110010011 0.1010010011 *
0.1110010010 0.1010010010 *
0.1110010110 0.1010010110 *
0.1110010111 0.1010010111 *
0.1110010101 0.1010010101 *
0.1110010100 0.1010011100 *	A'
0.1110011100 0.1010010100 *	A'
0.1110011101 0.1010011101 *
0.1110011111 0.1010011111 *
0.1110011110 0.1010011110 *
0.1110011010 0.1010011010 *
0.1110011011 0.1010011011 *
0.1110011001 0.1010011001 *
0.1110011000 0.1010011000 *
0.1110001000 0.1010001000 *
0.1110001001 0.1010001001 *
0.1110001011 0.1010001011 *
0.1110001010 0.1010001010 *
0.1110001110 0.1010001110 *
0.1110001111 0.1010001111 *
0.1110001101 0.1010001101 *
0.1110001100 0.1010001100 *
0.1110000100 0.1010000100 *
0.1110000101 0.1010000101 *
0.1110000111 0.1010000111 *
0.1110000110 0.1010000110 *
0.1110000010 0.1010000010 *
0.1110000011 0.1010000011 *
0.1110000001 0.1010000001 *
0.1110000000 0.1010000000 *
0.1010000000 0.1110000000 *
0.1010000001 0.1110000001 *
0.1010000011 0.1110000011 *
0.1010000010 0.1110000010 *
0.1010000110 0.1110000110 *
0.1010000111 0.1110000111 *
0.1010000101 0.1110000101 *
0.1010000100 0.1110000100 *
0.1010001100 0.1110001100 *
0.1010001101 0.1110001101 *
0.1010001111 0.1110001111 *
0.1010001110 0.1110001110 *
0.1010001010 0.1110001010 *
0.1010001011 0.1110001011 *
0.1010001001 0.1110001001 *
0.1010001000 0.1110001000 *
0.1010011000 0.1110011000 *
0.1010011001 0.1110011001 *
0.1010011011 0.1110011011 *
0.1010011010 0.1110011010 *
0.1010011110 0.1110011110 *
0.1010011111 0.1110011111 *
0.1010011101 0.1110011101 *
0.1010011100 0.1110010100 *	A'
0.1010010100 0.1110011100 *	A'
0.1010010101 0.1110010101 *
0.1010010111 0.1110010111 *
0.1010010110 0.1110010110 *
0.1010010010 0.1110010010 *
0.1010010011 0.1110010011 *
0.1010010001 0.1110010001 *
0.1010010000 0.1110010000 *


B
0.0111001000 0.0101001000 *
0.0111001001 0.0101001001 *
0.0111001011 0.0101001011 *
0.0111001010 0.0101001010 *
0.0111001110 0.0101001110 *
0.0111001111 0.0101001111 *
0.0111001101 0.0101001101 *
0.0111001100 0.0101001100 *
0.0111000100 0.0101000100 *
0.0111000101 0.0101000101 *
0.0111000111 0.0101000111 *
0.0111000110 0.0101000110 *
0.0111000010 0.0101000010 *
0.0111000011 0.0101000011 *
0.0111000001 0.0101000001 *
0.0111000000 0.0101000000 *
0.0101000000 0.0111000000 *
0.0101000001 0.0111000001 *
0.0101000011 0.0111000011 *
0.0101000010 0.0111000010 *
0.0101000110 0.0111000110 *
0.0101000111 0.0111000111 *
0.0101000101 0.0111000101 *
0.0101000100 0.0111000100 *
0.0101001100 0.0111001100 *
0.0101001101 0.0111001101 *
0.0101001111 0.0111001111 *
0.0101001110 0.0111001110 *
0.0101001010 0.0111001010 *
0.0101001011 0.0111001011 *
0.0101001001 0.0111001001 *
0.0101001000 0.0111001000 *


C
0.0011100100 0.0010100100 *
0.0011100101 0.0010100101 *
0.0011100111 0.0010100111 *
0.0011100110 0.0010100110 *
0.0011100010 0.0010100010 *
0.0011100011 0.0010100011 *
0.0011100001 0.0010100001 *
0.0011100000 0.0010100000 *
0.0010100000 0.0011100000 *
0.0010100001 0.0011100001 *
0.0010100011 0.0011100011 *
0.0010100010 0.0011100010 *
0.0010100110 0.0011100110 *
0.0010100111 0.0011100111 *
0.0010100101 0.0011100101 *
0.0010100100 0.0011100100 *


D
0.0001110010 0.0001010010 *
0.0001110011 0.0001010011 *
0.0001110001 0.0001010001 *
0.0001110000 0.0001010000 *
0.0001010000 0.0001110000 *
0.0001010001 0.0001110001 *
0.0001010011 0.0001110011 *
0.0001010010 0.0001110010 *
0.1001010010 0.1001110010 *
0.1001010011 0.1001110011 *
0.1001010001 0.1001110001 *
0.1001010000 0.1001110000 *
0.1001110000 0.1001010000 *
0.1001110001 0.1001010001 *
0.1001110011 0.1001010011 *
0.1001110010 0.1001010010 *

E
0.0000111001 0.0000101001 *
0.0000111000 0.0000101000 *
0.0000101000 0.0000111000 *
0.0000101001 0.0000111001 *
0.0100101001 0.0100111001 *
0.0100101000 0.0100111000 *
0.0100111000 0.0100101000 *
0.0100111001 0.0100101001 *
0.1100111001 0.1100101001 *
0.1100111000 0.1100101000 *
0.1100101000 0.1100111000 *
0.1100101001 0.1100111001 *
0.1000101001 0.1000111001 *
0.1000101000 0.1000111000 *
0.1000111000 0.1000101000 *
0.1000111001 0.1000101001 *

F
0.0000011100 0.0000010100 *
0.0000010100 0.0000011100 *
0.0010010100 0.0010011100 *
0.0010011100 0.0010010100 *
0.0110011100 0.0110010100 *
0.0110010100 0.0110011100 *
0.0100010100 0.0100011100 *
0.0100011100 0.0100010100 *
0.1100011100 0.1100010100 *
0.1100010100 0.1100011100 *
0.1000010100 0.1000011100 *
0.1000011100 0.1000010100 *


A	00.1x100hhhhh	30	x2	(exc A')
A'	00.1x1001y100	2	x2
B	0.01x100hhhh	16	x2
C	0.001x100hhh	8	x2
D	0.h001x100hh	8	x2
E	0.hh001x100h	8	x2
F	0.hhh001x100	6	x2	(exc A')