Essays/Base Spectrum
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Base Spectrum is a working code name for a density plot of a base representation of a number or a sequence of numbers.
Base 2 spectrum may be called binary spectrum, e.g.
Binary spectrum of the natural sequence:
require 'viewmat trig plot' viewmat |: #:i.128
Sierpinski Triangle fractal (, ,.~)^:n ,1 is also a Binary Spectrum of the Sloane's A001317
It is defined as "Pascal's triangle mod 2 converted to decimal"
#. |.2|!/~i.16 1 3 5 15 17 51 85 255 257 771 1285 3855 4369 13107 21845 65535
and can be obtained by recursive formula a(n+1) = a(n) XOR 2a(n)
viewmat #:(~:/&.#:@, +:)^:(<32) 1
Other binary spectra:
viewmat |: #: *: i.128 NB. squares
viewmat |: #: %: i.128 NB. square roots
viewmat |: #: 2^. 1+i.128 NB. log2 x
viewmat |: #: ^. 1+i.128 NB. ln x
viewmat |: #: ^ 1r32*i.128 NB. exp x
viewmat |: #: cosh 1r32*i:128 NB. cosh x
viewmat |: #: sinh 1r32*i:128 NB. sinh x
viewmat |: #: tan 1r16*i.128 NB. tan x
Base 3 spectrum may be called ternary spectrum.
Here is some derivations of ternary spectrum of the natural sequence.
viewmat +./\|:1=(6#3)#:i.3^6 NB. Cantor comb
viewmat +/\|:1=(6#3)#:i.3^6 NB. Cantor city
Same in 3D:
'wire;boxed 0;viewpoint 2 _1 1.2'plot +/\|:1=(6#3)#:i.3^6
See Also
- Scripts/Viewmat Spy
- Capture Graphics with media/platimg addon and precise resizing
Contributed by Oleg Kobchenko.