03_residual_grid.tex
Paper X: Universal Residual Seeds and Conditional Occupied-System Completion
03_residual_grid.tex
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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\scriptsize] at (2.2,4.15) {$0$};
4 \node[font=\small,align=center,font=\scriptsize] at (3.36,4.15) {$1$};
5 \node[font=\small,align=center,font=\scriptsize] at (4.52,4.15) {$2$};
6 \node[font=\small,align=center,font=\scriptsize] at (5.68,4.15) {$3$};
7 \node[font=\small,align=center,font=\scriptsize] at (6.84,4.15) {$4$};
8 \node[font=\small,align=center,font=\scriptsize] at (8,4.15) {$5$};
9 \node[font=\small,align=center,font=\scriptsize] at (9.16,4.15) {$6$};
10 \node[font=\small,align=center,font=\scriptsize] at (10.32,4.15) {$7$};
11 \node[font=\small,align=center,font=\scriptsize] at (11.48,4.15) {$8$};
12 \node[font=\small,align=center,font=\small] at (0.85,3.25) {$r=0$};
13 \path[draw=black!35,fill=white] (1.65,2.83) rectangle (2.75,3.63);
14 \node[font=\small,align=center] at (2.2,3.23) {$0$};
15 \path[draw=black!35,fill=white] (2.81,2.83) rectangle (3.91,3.63);
16 \node[font=\small,align=center] at (3.36,3.23) {$3$};
17 \path[draw=black!35,fill=white] (3.97,2.83) rectangle (5.07,3.63);
18 \node[font=\small,align=center] at (4.52,3.23) {$6$};
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20 \node[font=\small,align=center] at (5.68,3.23) {$9$};
21 \path[draw=black!35,fill=white] (6.29,2.83) rectangle (7.39,3.63);
22 \node[font=\small,align=center] at (6.84,3.23) {$12$};
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24 \node[font=\small,align=center] at (8,3.23) {$15$};
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26 \node[font=\small,align=center] at (9.16,3.23) {$18$};
27 \path[draw=black!35,fill=white] (9.77,2.83) rectangle (10.87,3.63);
28 \node[font=\small,align=center] at (10.32,3.23) {$21$};
29 \path[draw=black!35,fill=white] (10.93,2.83) rectangle (12.03,3.63);
30 \node[font=\small,align=center] at (11.48,3.23) {$24$};
31 \node[font=\small,align=center,font=\small] at (0.85,2.2) {$r=1$};
32 \path[draw=black!35,fill=black!10] (1.65,1.78) rectangle (2.75,2.58);
33 \node[font=\small,align=center] at (2.2,2.18) {$1$};
34 \path[draw=black!35,fill=black!10] (2.81,1.78) rectangle (3.91,2.58);
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38 \path[draw=black!35,fill=black!10] (5.13,1.78) rectangle (6.23,2.58);
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40 \path[draw=black!35,fill=black!10] (6.29,1.78) rectangle (7.39,2.58);
41 \node[font=\small,align=center] at (6.84,2.18) {$13$};
42 \path[draw=black!35,fill=black!10] (7.45,1.78) rectangle (8.55,2.58);
43 \node[font=\small,align=center] at (8,2.18) {$16$};
44 \path[draw=black!35,fill=black!10] (8.61,1.78) rectangle (9.71,2.58);
45 \node[font=\small,align=center] at (9.16,2.18) {$19$};
46 \path[draw=black!35,fill=black!10] (9.77,1.78) rectangle (10.87,2.58);
47 \node[font=\small,align=center] at (10.32,2.18) {$22$};
48 \path[draw=black!35,fill=black!10] (10.93,1.78) rectangle (12.03,2.58);
49 \node[font=\small,align=center] at (11.48,2.18) {$25$};
50 \node[font=\small,align=center,font=\small] at (0.85,1.15) {$r=2$};
51 \path[draw=black!35,fill=white] (1.65,0.73) rectangle (2.75,1.53);
52 \node[font=\small,align=center] at (2.2,1.13) {$2$};
53 \path[draw=black!35,fill=white] (2.81,0.73) rectangle (3.91,1.53);
54 \node[font=\small,align=center] at (3.36,1.13) {$5$};
55 \path[draw=black!35,fill=white] (3.97,0.73) rectangle (5.07,1.53);
56 \node[font=\small,align=center] at (4.52,1.13) {$8$};
57 \path[draw=black!35,fill=white] (5.13,0.73) rectangle (6.23,1.53);
58 \node[font=\small,align=center] at (5.68,1.13) {$11$};
59 \path[draw=black!35,fill=white] (6.29,0.73) rectangle (7.39,1.53);
60 \node[font=\small,align=center] at (6.84,1.13) {$14$};
61 \path[draw=black!35,fill=white] (7.45,0.73) rectangle (8.55,1.53);
62 \node[font=\small,align=center] at (8,1.13) {$17$};
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64 \node[font=\small,align=center] at (9.16,1.13) {$20$};
65 \path[draw=black!35,fill=white] (9.77,0.73) rectangle (10.87,1.53);
66 \node[font=\small,align=center] at (10.32,1.13) {$23$};
67 \path[draw=black!35,fill=white] (10.93,0.73) rectangle (12.03,1.53);
68 \node[font=\small,align=center] at (11.48,1.13) {$26$};
69 \node[font=\small,align=center] at (7,4.65) {$x=3q+r\pmod{27}$: columns are higher-digit addresses $q$};
70 \node[font=\small,align=center,font=\footnotesize] at (7,0.05) {Adding $3$ moves within one row. Adding $1$ can change the row.};
71 \end{tikzpicture}
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