fix typos in 4.appendix

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queue-miscreant 2025-03-06 01:44:14 -06:00
parent f5249fe753
commit ed3c8a331c
3 changed files with 13 additions and 13 deletions

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@ -233,7 +233,7 @@ Perhaps it is still unconvincing that expanding the integers in this way gives s
In fact, since the expansions are in binary or (balanced) ternary, the integers should just
be a subset of the 2-adics or 3-adics.
Still, wanted to see what these numbers actually "look" like, so I whipped up an interactive diagram.
Still, I wanted to see what these numbers actually "look" like, so I whipped up an interactive diagram.
You should definitely see [this page](/interactive/adic/) for more information, but
the gist is that *p*-adics can be sent into the complex plane in a fractal-like way.
@ -258,10 +258,15 @@ Within these two clusters, the rightmost portion of them appears to be the same
If you try switching between the *κ*-adic options, you can even see the smaller
and larger shapes changing in the same way as one another.
If you prefer not to use JavaScript, I also prepared a [Python script](./kadic.py) to run locally[^1].
You can trace out images from this version can be seen below:
This is actually great news -- if you switch between the *κ*-adics and the "random binary" option,
you can see that the latter option tends to the same pattern as the 2-adics.
Thus, even if the expansions for the integers are individually chaotic, together they possess a
much different structure than pure randomness.
:::: {.row .centered}
If you prefer not to use JavaScript, I also prepared a [Python script](./kadic.py) using Matplotlib.[^1]
Here are a couple of screenshots from the script, which demonstrates the self-similarity mentioned above.
:::: {.row}
::: {layout-ncol="2"}
![`quotRem`](./cendree_quotrem_fractal.png)
@ -271,10 +276,5 @@ You can trace out images from this version can be seen below:
Clusters of *κ*-adics, with self-similar patterns boxed in red.
::::
This is actually great news -- if you switch between the *κ*-adics and the "random binary" option,
you can see that the latter option tends to the same pattern as the 2-adics.
Thus, even if the expansions for the integers are individually chaotic, together they possess a
much different structure than pure randomness.
[^1]: You will also need the [`divMod`](./cendree_DivMod_count_1024_256_digits.csv)
and [`quotRem`](./cendree_QuotRem_count_1024_256_digits.csv) data files.

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@ -23,9 +23,9 @@ import { expansions as oldExpansions } with { base as base } from "../../../../i
expansionsOrAdics = baseSelector == "b-adic"
? oldExpansions
: baseSelector == "κ-adic, balanced"
? adicExpansionsDivMod
: baseSelector == "κ-adic, binary"
? adicExpansionsQuotRem
: baseSelector == "κ-adic, binary"
? adicExpansionsDivMod
: d3.range(adicExpansionsQuotRem.length / 10).map(() => d3.range(15).map(() => +(Math.random() > 0.5)))
import { plot } with {