fix typos in 4.appendix

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

File diff suppressed because one or more lines are too long

View File

@ -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 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. 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 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. 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 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. 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]. This is actually great news -- if you switch between the *κ*-adics and the "random binary" option,
You can trace out images from this version can be seen below: 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"} ::: {layout-ncol="2"}
![`quotRem`](./cendree_quotrem_fractal.png) ![`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. 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) [^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. and [`quotRem`](./cendree_QuotRem_count_1024_256_digits.csv) data files.

View File

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