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This page introduces a large number of "alternative writing systems" for the English language, some of which have some interesting geometrical properties.
Some of these geometric writing systems gives more freedom on the letters' size, position, or shapes, such as Exprish or Circular Gallifreyan. Others may used a fixed shape for each letter, such as Graph Script and ABB Gallifreyan.
In this challenge, you are given a code that should be copied and pasted into Desmos. Then, try to read what you see on the graph as a text in one of the conscript ciphers.
You may also try transcribing a piece of text you like in one of the conscript ciphers using math equations, and copying the equations from Desmos line by line into a text file.
For example, this code decodes to "ColorfulGalaxy" in Circular Gallifreyan.
x^{2}+y^{2}=100\ \left\{x<10-\frac{y}{\sqrt{3}}\right\}\left\{y<\frac{159}{16}\right\}\left\{14x+8y>-160\right\}
x^{2}+\left(y+7\right)^{2}=5
\left(x-6\right)^{2}+\left(y+4\right)^{2}=5
\left(x-15\right)^{2}+\left(y-5\sqrt{3}\right)^{2}=100\left\{x<10-\frac{y}{\sqrt{3}}\right\}
x^{2}+\left(y-8\right)^{2}=5\ \left\{y<\frac{159}{16}\right\}
\left(x+6\right)^{2}+\left(y-4\right)^{2}=5
\left(x+7\right)^{2}+\left(y+4\right)^{2}=5\left\{14x+8y>-160\right\}
x^{2}+y^{2}=18
x^{2}+\left(y+2\right)^{2}=4
\left(x-3\right)^{2}+\left(y-3\right)^{2}=4
\left(x+4\right)^{2}+y^{2}=4
y=2x+8\left\{-5<y<6\right\}\left\{\left(x+7\right)^{2}+\left(y+4\right)^{2}>5\right\}
\left(x+y-7\right)\left(x+y-8\right)=0\left\{x^{2}+\left(y-8\right)^{2}>5\ \right\}\left\{\left(x-3\right)^{2}+\left(y-3\right)^{2}>4\right\}\left\{4<y<8\right\}
\left(x-2\right)^{2}+\left(y+6\right)^{2}=0.25
\left(x-7\right)^{2}+\left(y+2\right)^{2}=0.25
x^{2}+\left(y-8\right)^{2}=0.25
x=0\left\{8.5<y<12\right\}
\left(x+6\right)^{2}+\left(y+9\right)^{2}=0.25
\left(x-3\right)^{2}+\left(y+4\right)^{2}=0.25
\left[\left(-6,5\right),\left(-5,3\right),\left(-7,3\right),\left(-3,1\right),\left(-3,-1\right),\left(0,-1\right),\left(1,-3\right),\left(-1,-3\right),\left(1,-7\right),\left(-1,-7\right),\left(0,-6\right),\left(0,-8\right),\left(6,-3\right),\left(7,-5\right),\left(5,-5\right),\left(6,6\right),\left(7,4\right),\left(8,3\right)\right]
x^{2}+y^{2}=144
x^{2}+y^{2}=160Here is the first task:
u=0
f_{rx}\left(x,y,\theta\right)=x\cos\theta+y\sin\theta
f_{ry}\left(x,y,\theta\right)=y\cos\theta-x\sin\theta
f_{mod}\left(x,m\right)=\frac{m}{\pi}\arctan\left(\tan\frac{x\pi}{m}\right)
g_{n}\left(x,y\right)=\sqrt{x^{2}+y^{2}}
g_{t}\left(x,y\right)=\operatorname{abs}\left(x\right)+\operatorname{abs}\left(y\right)
g_{s1}\left(x,y\right)=\left(x^{2}-y^{2}\right)f_{rx}\left(x,y,0\right)
g_{sh1}\left(x,y\right)=f_{rx}\left(x,y,0\right)f_{rx}\left(x,y,-\frac{\pi}{16}\right)f_{rx}\left(x,y,-\frac{\pi}{8}\right)f_{rx}\left(x,y,-\frac{3\pi}{16}\right)f_{rx}\left(x,y,-\frac{\pi}{4}\right)
g_{k}\left(x,y\right)=f_{ry}\left(x,y,0\right)f_{rx}\left(x,y-1,-\frac{\pi}{6}\right)\left(x^{2}+y^{2}\right)
g_{j}\left(x,y\right)=f_{ry}\left(x,y,0\right)f_{rx}\left(x,y+1,\frac{\pi}{6}\right)\left(g_{n}\left(x+\frac{1}{3\sqrt{3}},y+\frac{1}{3\sqrt{3}}\right)-\frac{1}{3\sqrt{6}}\right)
g_{l}\left(x,y\right)=\prod_{n=0}^{9}\left(y-n\right)
g_{w}\left(x,y\right)=f_{ry}\left(x,y,0\right)\left(y-\operatorname{abs}\left(x\right)+1\right)
y^{2}=484\left\{-6<x<12\right\}
\left(x+6\right)\left(x-12\right)=0\left\{\left|y\right|<x+22+6\right\}
y^{2}=121\left\{6<x<12\right\}
x=6\left\{y^{2}<121\right\}
y^{2}=16\left\{12<x<\frac{44}{3}\right\}
x=\frac{44}{3}\left\{y^{2}<16\right\}
10=g_{n}\left(x,y\right)\left\{x<-6\right\}
x+y=10\left\{f_{mod}\left(-u,16\right)<f_{mod}\left(y-x,16\right)+\left[-16,0,16\right]<f_{mod}\left(-u,16\right)+2\right\}\left\{x>6\right\}\left\{y>-4\right\}
f_{mod}\left(x-y,16\right)=f_{mod}\left(u-1,16\right)\left\{9<x+y<11\right\}\left\{6<x<\frac{44}{3}\right\}\left\{y>-4\right\}
f_{mod}\left(x-\frac{u}{2}-11.5,8\right)^{2}+f_{mod}\left(y+\frac{u}{2}+1.5,8\right)^{2}=0.5\ \left\{6<x<\frac{44}{3}\right\}\left\{y>-4\right\}\left\{8<x+y<12\right\}
g_{1}\left(x,y\right)=g_{n}\left(f_{rx}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right)-8,f_{ry}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right)\right)
\left[1,2\right]=g_{1}\left(x,y\right)
0=g_{s1}\left(f_{rx}\left(f_{rx}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right)-8,f_{ry}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right),-\frac{3\pi u}{64}\right),f_{ry}\left(f_{rx}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right)-8,f_{ry}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right),-\frac{3\pi u}{64}\right)\right)\left\{2>g_{1}\left(x,y\right)\right\}
f_{rx}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right)=8\left\{2<f_{ry}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right)<5\right\}
f_{ry}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right)=3\left\{7<f_{rx}\left(x,y,-\frac{\pi u}{16}-\frac{\pi}{8}\right)<9\right\}
14=x\left\{f_{mod}\left(\frac{u}{8},8\right)-2<f_{mod}\left(y,8\right)+\left[-16,-8,0,8,16\right]<f_{mod}\left(\frac{u}{8},8\right)+2\right\}\left\{y^{2}<16\right\}
f_{mod}\left(\frac{u}{8},8\right)=y\left\{13.5<x<14.5\right\}
0=g_{l}\left(x,6\left(f_{mod}\left(y-\frac{u}{8},8\right)\right)+10.5\right)\left\{13.625<x<13.875\right\}\left\{y^{2}<16\right\}
g_{n}\left(x-5,y-6\right)=\left[\frac{3}{2},2\right]
g_{sh1}\left(x-5,y-6\right)=0\left\{g_{n}\left(x-5,y-6\right)<\frac{3}{2}\right\}
x=5\left\{8<y<10\right\}
y=9\left\{4<x<6\right\}
\left[\left(0,0\right)\right]Hint: It's written in Timescript.
Notes on the code in the first task:
1. The "u" variable indicates time. Click the button below the play button on Desmos and set the cycling mode to "one-way cycle" (the second option) instead of "round-trip cycle" in order that the shapes do not travel in the wrong direction. The period of the rotation is 128 in this case.
2. The reason why the time variable is not named "t" is that "t" is ambiguous. If "t" is used, then Desmos may wrongly render the /h/ (h in house) phoneme symbol as lines or circles instead of the expected dots in the chart.
3. The built-in function "mod" on Desmos proved to be buggy. Therefore, the self-defined "f_mod" function is used, though it doesn't actually work the same way as the "mod" function.
4. If you want to transcribe your own piece of text, we suggest that you should not make the left side of the equation consist of a single variable name or a single function call unless when you are actually defining variables or functions. Try swapping the sides of the equations. See also this post.
5. Please zoom out a little to see the whole shape. However, for some reason (probably a bug), the symbol representing the "l" in the last word may flicker (or simply vanish) even when the graph is zoomed out slightly.
6. If you want to transcribe your text in Timescript, you can use the following template:
u=0
f_{rx}\left(x,y,\theta\right)=x\cos\theta+y\sin\theta
f_{ry}\left(x,y,\theta\right)=y\cos\theta-x\sin\theta
f_{mod}\left(x,m\right)=\frac{m}{\pi}\arctan\left(\tan\frac{x\pi}{m}\right)
g_{n}\left(x,y\right)=\sqrt{x^{2}+y^{2}}
g_{t}\left(x,y\right)=\operatorname{abs}\left(x\right)+\operatorname{abs}\left(y\right)
g_{s1}\left(x,y\right)=\left(x^{2}-y^{2}\right)f_{rx}\left(x,y,0\right)
g_{sh1}\left(x,y\right)=f_{rx}\left(x,y,0\right)f_{rx}\left(x,y,-\frac{\pi}{16}\right)f_{rx}\left(x,y,-\frac{\pi}{8}\right)f_{rx}\left(x,y,-\frac{3\pi}{16}\right)f_{rx}\left(x,y,-\frac{\pi}{4}\right)
g_{k}\left(x,y\right)=f_{ry}\left(x,y,0\right)f_{rx}\left(x,y-1,-\frac{\pi}{6}\right)\left(x^{2}+y^{2}\right)
g_{j}\left(x,y\right)=f_{ry}\left(x,y,0\right)f_{rx}\left(x,y+1,\frac{\pi}{6}\right)\left(g_{n}\left(x+\frac{1}{3\sqrt{3}},y+\frac{1}{3\sqrt{3}}\right)-\frac{1}{3\sqrt{6}}\right)
g_{l}\left(x,y\right)=\prod_{n=0}^{9}\left(y-n\right)
g_{w}\left(x,y\right)=f_{ry}\left(x,y,0\right)\left(y-\operatorname{abs}\left(x\right)+1\right)xp8_4b23021eaz57840c4d2
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