New Post Tornado

Author: MinaBasilious

content/posts/tornado-of-lines.md

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+date = '2026-03-02T01:26:26+02:00'
+draft = false
+title = 'Tornado of Lines'
+description = ''
+thumbnail = '/images/tornadothmb.svg'
+showThumbnail = false
+tags = ['Lines']
+# coauthors = [
+#   { name = 'Jane Doe', link = 'mailto:jane@example.com' },
+# ]
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+
+![](/images/tornado.gif)
+This graph is defined by bunch of lines by defining two points, the start and the end, and then connect them.
+
+Each pair of points is defined by four functions which is
+$$X_1(n)=\sin\left(\frac{2\pi n}{1000}\right)-\cos\left(\frac{\pi n}{1000}\right)$$
+$$Y_{1}(n)=\left(\cos\left(\frac{2\pi n}{1000}+\frac{2\pi}{5}\right)\right)^{3}$$
+$$X_{2}(n)=\sin\left(\frac{5\pi n}{1000}+\frac{\pi}{3}\right)$$
+$$Y_{2}(n)=\sin\left(\frac{\pi n}{1000}+\frac{\pi}{10}\right)$$
+
+Hence each line as a function, $l:\mathbb N^+s \times \mathbb R ^{+}\to \mathcal P(\mathbb R^2)$, is defined as
+$$l(k,o)=\set{\left(1-t\right)\left(X_{1}\left(k\right),Y_{1}\left(k\right)\right)+t\left(X_{2}\left(k\right),Y_{2}\left(k\right)\right) \in \mathbb R^2 \mid t \in [0,o]}$$
+
+At the end, the graph is
+$$G(o)=\bigcup _{k=1}^{1000}l(k,o)$$
+and animation is just varying $o$ between $0$ and $1$.