morse.mac

/*
http://fraktal.republika.pl/mset_external_ray_f1_2.html

Feigenbaum-Myrberg point = -1.4011551890 ... 
> What external rays land on the Myrberg-Feigenbaum point ?
The candidate angle form above is obtained by using the substitution
0 -> 01 and 1 -> 10 repeatedly:
0
01
0110
01101001
0110100110010110
...
But it is not known whether the rays actually lands; maybe M is not locally connected at the Feigenbaum point and some long decorations are shielding it from external rays.( Wolf Jung )

upper external angles of roots are:
angle(c1) = 0.(01)			= 1/3
angle(c2) = 0.(0110)			= 6/15
angle(c3) = 0.(01101001)		= 7/17
angle(c4) = 0.(0110100110010110)	= 106/257

...
One can compute it using Maxima CAS program :



t1 = 0.(01)
t2 = 0.(0110)
t3 = 0.(01101001)
t4 = 0.(0110100110010110)
t5 = 0.(01101001100101101001011001101001)
t6 = 0.(0110100110010110100101100110100110010110011010010110100110010110)
t7 = 0.(01101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001)
t8 = 0.(0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010010110011010010110100110010110100101100110100110010110011010010110100110010110)
t9 = 0.(0110100110010110100101100110100110010110011010010110100110010110100101100110100101101001100101100110100110010110100101100110100110010110011010010110100110010110011010011001011010011100110100101101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001011010011001011010010110011010011001011001101001011010011001011001101001100101101001011001101001100101100110100101101001100101101001011001101001011010011001011001101001100101101001011001101001)



https://en.wikipedia.org/wiki/Thue%E2%80%93Morse_sequence

*/
kill(all);
remvalue(all);


f(x):=if (x=0) then [0,1] else [1,0];
compile(all);


a:[];
a:endcons([0],a);


for n:2 thru 10 step 1 do (
a:endcons([],a),
for x in a[n-1] do (a[n]:endcons(first(f(x)),a[n]),
                  a[n]:endcons(second(f(x)),a[n])),

print(n,"0.(",a[n], ")")


);