The Feigenbaum constants came into existence by way of a number of rejection letters from the publisher. His ideas were hard to explain let alone prove. The first constant has an infinite decimal expansion:
q = 4.669201609102…
We use this constant, with a formula to find “quiet” places within the logistic map. At these places, there is a cricket sound; but just a decimal place away, there will be incoherent noise.
Coherent and Chaotic sound files
At the bifurcation parameter
Same parameter offset by 0.1
Since there are 5000 data points, a script must be used rather than just clicking the mouse or touch pad.
Warning:
Later Versions of Praat are not backward compatible with earlier versions.
Curly quotes from Word or the internet don’t work in your text file, these, ” “, are not the same as in the program below.
;;;;; climatehoax.ca@gmail.com ;;;;
do ("Create AmplitudeTier...", "empty", 0, 1)
ainf = 3.569946
q = 4.669201609
x0 = 0.5
t0 = 0
c = 2.6327
n = 3
add_chaos = 0.0
;add_chaos = 0.1
a = ainf - c*q^(-n) + add_chaos
writeInfoLine ("Bifurcation Parameter ", a, "for n = ", n )
;;; logistic map, points added to Tier
for i from 1 to 5000
le[i] = (a * x0 * (1 - x0))
x = a* x0* (1-x0)
do ("Add point...", t0, le[i])
t0 = t0 + 0.00025
x0 = x
endfor
do ("Create Sound as pure tone...", "tone",
... 1, 0, 1, 44100, 17, 0.2, 0.01, 0.01)
selectObject ("AmplitudeTier empty")
plusObject ("Sound tone")
do ("Multiply")
selectObject ("Sound tone_amp")
do ("Filter (pass Hann band)...", 500, 1000, 100)
Play
Ape Town 