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RHOS
January 1, 2025
Suppose a stack
𝕊
and a set of functions
ℱ
that operate thereon—poping of
values for use as inputs, and putting back on as corresponding outputs. Suppose
further that
ℱ
, among other functions, contains those listed in
Listing 1
.
:
ₙ
⊟
⇡
⧻
⌊
⌵
≡
duplicate
flip
power
couple
range
shape
floor
abs
map
Listing 1: A few of the functions in
ℱ
Each a conscice incantation, performed on the arbitrarily many dimensions of
an input. Lastly, recall that an
𝑛
×
𝑛
Gaussian kernel can be constructed using
the Radial Basis Function in
Eq. 1
𝐾
𝑖
,
𝑗
=
exp
(
−
(
𝑖
−
𝑗
)
2
2
𝜎
2
)
(1)
where
𝑖
,
𝑗
are indices of the kernel relative to its center, which, using the using
the functions in
Listing 1
can be expressed as per
Listing 2
R ← ⁿ : e ¯ ÷ × 2 ⁿ 2 : √ / + ⁿ 2 ⌵
G ← ≡ ₁ R ⌵ - ⌊ ÷ 2 ⊸ ⧻ ⇡ ⊟ . : ₙ e .
D ← ÷ ⊸ ( / ↥ / ↥ ) √ ⌵ - ⊸ ↻ 1
Listing 2: Radial basis function (top), Gaussian kernel function (middle), and
discrete two dimensional derivative function (bottom)
The code
G 512
and
D G 512
, thus genertaes the left and right subplots of
Figure 1
respectively
Figure 1: A Gaussian kernel (left) and its associated derivative (right)
For the scientifically inclined, these Gaussian gradients might bring to mind
the notion of orbitals, and probability density functions (indeed that is in fact
what a Gaussian
is
). However—and perhaps more something-somethingly—the
relationship between
Listing 2
and
Figure 1
is of an Asemic nature, echoing
works like the Codex Seraphinianus
[1]
. To put it bluntly, Uiua’s—the language
of which we speak—is rivavled in its inscruitability only by its expressiveness,
which is to say very.
The artifacts produced—kernels, gradients, figures—are legible to those initi
ated in scientific the hypthetical scientific ritual to which they could have
belonged, and yet the code that conjures them echoes the inscrutable glyphs
of the Codex Seraphinianus, where language teeters on the edge aesthtics, but
quite far from meaning.
REFERENCES
[1]
L. Serafini,
Codex Seraphinianus. 2
. Milano: Ricci, 1983.