Created
January 29, 2019 11:03
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Farey creates an ordered List containing decimal representations of a full Farey sequence up to F(n).
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/* | |
Farey creates an ordered List containing decimal representations of a full Farey sequence up to F(n). | |
You can use my Rationalize class for conversion to rational list. | |
(translated from the Python example on Wikipedia) | |
*/ | |
Farey { | |
*new { |n = 5| | |
var farey = List(); | |
var a, b, c, d, k; | |
#a, b, c, d = [0, 1, 1, n]; | |
while ({ c <= n }, | |
{ | |
k = floor((n + b) / d); | |
#a, b, c, d = [c, d, (k * c - a), (k * d - b)]; | |
/*convert to decimals and put in the list. | |
at least six-decimal precision is required for .asFraction to convert back to rationals*/ | |
farey.add((a/b).round(0.000001)); | |
postf("%/%",a,b); // post the rationals | |
post(" "); | |
}; | |
); | |
postln("************"); | |
// return the decimal list | |
^farey | |
} | |
} |
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