JMD ex. 4.3: rho1=(5-sqrt5)/10, rho2=sqrt5/10 (sum 1/2)
   rho1=0.276393 rho2=0.223607 ; exact families (period, measure fraction, (n,m1,m2,v)): [(4, 0.6833, (2, 2, 2, 1)), (14, 0.3167, (3, 3, 3, 1))] ; all periodic predicted: True
   float simulation, 3000 random starts: [(14, 962), (4, 2038)]   -> OK
source Ex. 3: rho1=1/4, rho2=1/sqrt30
   rho1=0.250000 rho2=0.182574 ; exact families (period, measure fraction, (n,m1,m2,v)): [(6, 0.1349, (1, 2, 0, 0))] ; all periodic predicted: False
   float simulation, 3000 random starts: [('non-closing', 2614), (6, 386)]   -> OK
rho1+rho2=1/2, rho2=(sqrt2-1)/4
   rho1=0.448223 rho2=0.051777 ; exact families (period, measure fraction, (n,m1,m2,v)): [(50, 0.3198, (9, 9, 9, 1)), (28, 0.6802, (10, 10, 10, 1))] ; all periodic predicted: True
   float simulation, 3000 random starts: [(28, 2028), (50, 972)]   -> OK
rho1+2rho2=1 (alpha+2lam=2), lam=(sqrt2+3)/8
   rho1=0.448223 rho2=0.275888 ; exact families (period, measure fraction, (n,m1,m2,v)): [(3, 0.6723, (2, 1, 2, 1))] ; all periodic predicted: False
   float simulation, 3000 random starts: [('non-closing', 956), (3, 2044)]   -> OK
2rho1+rho2=1 (2alpha+lam=2), lam=(sqrt2+3)/8
   rho1=0.362056 rho2=0.275888 ; exact families (period, measure fraction, (n,m1,m2,v)): [(3, 0.1553, (2, 2, 1, 1))] ; all periodic predicted: False
   float simulation, 3000 random starts: [('non-closing', 2504), (3, 496)]   -> OK
rho1+3rho2=1/2 (alpha+3lam=1), lam=(sqrt2-1)/3 [N=7: no family]
   rho1=0.292893 rho2=0.069036 ; exact families (period, measure fraction, (n,m1,m2,v)): [] ; all periodic predicted: False
   float simulation, 3000 random starts: [('non-closing', 3000)]   -> OK
rho1=1/3 (alpha=2/3), lam=(sqrt2-1)/2 [lam<1/3]
   rho1=0.333333 rho2=0.103553 ; exact families (period, measure fraction, (n,m1,m2,v)): [(5, 0.1893, (2, 3, 0, 0))] ; all periodic predicted: False
   float simulation, 3000 random starts: [('non-closing', 2397), (5, 603)]   -> OK
rho1+rho2=3/10 (alpha+lam=3/5), lam=(sqrt3-1)/4
   rho1=0.208494 rho2=0.091506 ; exact families (period, measure fraction, (n,m1,m2,v)): [(22, 0.4904, (3, 5, 5, 1)), (68, 0.5096, (18, 30, 30, 5))] ; all periodic predicted: True
   float simulation, 3000 random starts: [(22, 1452), (68, 1548)]   -> OK
ALL OK
