[seqfan] Re: Anyone have a 3-D "Ulam" spiral?

Neil Fernandez primeness at borve.org
Wed Apr 28 09:52:56 CEST 2021


If we define a 3D Ulam spiral as having to grow like a cube rather than
a sphere, there is a nice interpretation in terms of colours. Instead of
the usual RGB space with 256^3 points, define an "n-rgb" space where
each coordinate is between -n and n. Then every point in the n-shell of
the 3D Ulam spiral corresponds to a colour in n-rgb, and each of those
colours is a tint or a shade (if it's on exactly 1 plane), or else a hue
(if it's on the edge where a plane of tints meets a plane of shades);
there are no tones. So in a sense what we're doing is ordering a
toneless colour space for arbitrary n (and also requiring a nice rule
for getting from one space to the next when n is cranked up and the
points we got for all smaller values of n now get reassigned to tones).


Neil Fernandez

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