Though hardly useful for most, pellish generates series of Pell-like numbers
based on minimum, maximum, and required values supplied by the user. Meaning
that at least one of the series will contain the required value, and all
values will be within the minimum and maximum specified. I find such a
sequence useful in publication design, in fact in the design of many things.
Typical python setup.py install should suffice.
pellish -h should show you the help screen.
pellish min req max creates a pellish matrix, where min is the minimum
value in any series, req appears in at least one series, and max is
the maximum value in all series.
pellish ... -t shows 'triplets' (three adjacent numbers, a, b, c
where c / a = 1 + √2, c / b = √2 or (1 + √2) / √2)
pellish ... -d 'unravels' the diagonals of the series
pellish ... -c -f PATH writes the pellish matrix to a CSV file located
at PATH.
pellish 1 29 500 will generate the Pell series up to 408, and then
a matrix of Pell-like series that contain the differences of the prior
series.
pellish 2 6 500 will do the same but starting with the Pell-Lucas series.
pellish 0 1 1000 will fail. Miserably.
pellish generates an initial Pell-like sequence based on your required
value, x*(n), by finding suitable values for x(n–1)* and x*(n–2), with
x(n)* = 2 * x*(n–1)* + x*(n–2), x(n–2)* >= min.
If possible, given your minimum, it will create multiple series of lesser values, based on the differences in the initial series. It will proceed with this until the initial value of a series is less than your specified minimum. Then it generates series of larger values, again based on differences of prior series, until it reaches your maximum value and/or a series of fewer than 3 values.
I've made up some silly lingo when I use Pell-like sequences in my design work. Very non-technical, but it's hard to understand some of the options and internal methods without understanding them.
Diagonals are series of numbers in the pellish matrix, whose pairs converge towards 1 : √2.
Triplets refer to groups of three adjacent values whose pairs are in the (approximate) proportions 1 : √2, 1 : (1 + √2) / √2. and 1 : 1 + √2
A minor triplet is one whose smallest numbers approximate the proportion 1 : √2.
A major triplet's largest numbers approximate 1 : √2.