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2+ date = ' 2026-02-22T14:11:29+02:00'
3+ draft = true
4+ title = ' Seraph'
5+ description = ' '
6+ thumbnail = ' /images/Seraph.svg'
7+ # showThumbnail = false
8+ tags = [' Complex Numbers' ,' Grid Transformation' ]
9+ # coauthors = [
10+ # { name = 'Jane Doe', link = 'mailto:jane@example.com' },
11+ # ]
12+ +++
13+
14+ "שְׂרָפִ֨ים עֹמְדִ֤ים ׀ מִמַּ֙עַל֙ ל֔וֹ שֵׁ֧שׁ כְּנָפַ֛יִם שֵׁ֥שׁ כְּנָפַ֖יִם לְאֶחָ֑ד בִּשְׁתַּ֣יִם ׀ יְכַסֶּ֣ה פָנָ֗יו וּבִשְׁתַּ֛יִם יְכַסֶּ֥ה רַגְלָ֖יו וּבִשְׁתַּ֥יִם יְעוֹפֵֽף׃
15+ `"
16+
17+ We define a grid by
18+ $$ P=\set{0.01(x+iy)\in\mathbb C\mid (x\in\mathbb Z\vee y\in\mathbb Z) ,200\le x,y\le200}. $$
19+
20+ Then we define a complex function,
21+ $$ f : P \subseteq \mathbb C \longrightarrow \mathbb C $$
22+ where,
23+ $$ f(z)= iz\sqrt i \ \mathrm{mod}(3,z) $$
24+ So, our graph is the image of this function.
25+ In other words,
26+ $$ G=f(P). $$
27+
28+ {{< video src="/videos/Seraph.mp4" width="75" >}}
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