extra extra revisions to polycount

polycount/3/index.qmd

@@ -13,10 +13,22 @@ categories:
   - phinary
   - binary
   - python
-execute:
 code-fold: true
 ---
 
+<style>
+  .cell-output-display .figure {
+    text-align: center;
+  }
+
+  /* #long-trunc-figures .figure-img { */
+  .figure-img {
+    max-width: 512px;
+    object-fit: contain;
+    height: 100%;
+  }
+</style>
+
 ```{python}
 #| echo: false
 
@@ -581,7 +593,7 @@ $$
 $$
 
 This neatly ties repeating spacings in with carries.
-^[Recall that when we naively computed ten in base phi, we got "10100.0100101010101010101".
+^[Recall that when we naively computed ten in base *φ*, we got "10100.0100101010101010101".
 After a certain point, this expansion alternates between 0 and 1. Assuming that this is true repetition
 and applying $10_\varphi = 1.\underline{01}_\varphi$, one obtains "10100.0101", which is canonical. ]
 

polycount/4/index.qmd

@@ -446,7 +446,7 @@ Unfortunately, this is not the case.
 All of the expansions above are identically four, and manipulating the digits directly would just
   give a different number.
 
-Instead, we could try representing "4" in a more direct manner
+Instead, we could try representing "4" in a more direct manner.
 There are a few other options available.
 
 - Add the nonrepeating part of the mixed balanced expansion of 4 with the
@@ -615,7 +615,7 @@ plt.title("DFT of $4_{\\kappa}$ after mapping $\\bar{1}$ to $1$")
 plt.plot(abs(np.fft.fft([abs(i) for i in cendree_adic_4[:256]]))[:129])
 ```
 
-If you look closely, you'll notice that this plot is a mirror of the other.
+If you look closely, you can notice that this plot is a mirror of the other.
 
 
 ### Longer Truncations
@@ -677,7 +677,7 @@ The [next post](../5) will return to integral sequences, and the patterns produc
 
     Recall that $3 = 10.02_{\kappa}$ and $4 = 11.02_{\kappa}$.
 
-    We can add two expansion together to produce a new valid expansion.
+    We can add two expansions together to produce a new valid expansion.
     Hence,
 
     :::: {.row layout-ncol="2"}

polycount/5/index.qmd

@@ -266,7 +266,7 @@ Because this operation is commutative, the shapes of the rectangles must agree a
 
 The shape of the rectangular blocks is somewhat odd.
 We can assess the number of terms the series "hangs" before progressing by looking at the
-  [*run lengths*](https://en.wikipedia.org/wiki/Run-length_encoding)).
+  [*run lengths*](https://en.wikipedia.org/wiki/Run-length_encoding).
 
 :::: {.row layout-ncol="1"}
 ::: {.row}
@@ -365,7 +365,9 @@ $$
 In this mapping, for $n = 2$, zero goes to red and one goes to cyan.
 The following is a 100x100 image of the multiplication table of $\oplus_\text{Zeck}$ from zero to ninety-nine.
 
-![](fibonacci_deficiency_mod_2.png){.image-wide}
+![
+   
+](fibonacci_deficiency_mod_2.png){.image-wide}
 
 
 ### Anima Moduli