given a vector v
v.sum -> the summation of elements
v.norm -> the normalization of V
the function is:
f(v) = v.norm * v.sum
example:
V = <1,1,3,-1>
V.sum = 4
V.norm = <0.288.., 0.288.., 0.866.., 0.288..>
f(V) = <1.15.., 1.15.., 3.46.., -1.15..>
Applying this recursively yields a set of vectors with the same normal and where the 'i'th element's magnitude is equal to the absolute value of the 'i-1'th element's sum. It came up whilst programing and I needed to name the function (and the series). It seems too trivial to not already have a name.