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Feigenbaum constants are traditionally calculated for period doubling cascades, but they can also be calculated for period tripling cascades (p=3^k):

delta = limit of ratio of successive sizes of components ~= 55.24719485586328460
alpha = limit of ratio of succesive f_c^(3^{k-1})(0) ~= 9.277343959121408190
mu_infinity = limit of successive component centers ~= 3.854077963590777589

(almost surely not accurate to all digits, my calculation methods are susceptible to rounding errors and I used only machine native double precision, with 53 mantissa bits)

I used my mandelbrot-numerics library to compute these in the z:=z^2+c representation, the ratios transfer without alteration to the x:=rx(1-x) representation. transferring between c and r can be done by:
r = 1 + sqrt(1 - 4 * c)
c = (1 - (r - 1) ^ 2) / 4

the period tripling corresponds to this location in the Mandelbrot set: mathr.co.uk/mandelbrot/web/#!q

reference: keithbriggs.info/documents/Kei

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