Background

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Math Machines

Bezier Curves

$$ \class{mj-green}{\vec c} - \class{mj-red}{\vec b} = \class{mj-blue}{\vec a} $$

$$ \class{mj-blue}{\vec a} + \class{mj-red}{\vec b} = \class{mj-green}{\vec c} $$

$$ \class{mj-red}{\vec b} - \class{mj-blue}{\vec a} = \class{mj-green}{\vec c} $$

Procedural Generation

$$ x $$

$$ x =\hspace{3 pt}? $$

function (x) { return x }

$$ x = $$

$$ \ldots $$ $$ -4 $$ $$ -3 $$ $$ -2 $$ $$ -1 $$ $$ 0 $$ $$ 1 $$ $$ 2 $$ $$ 3 $$ $$ 4 $$ $$ \ldots $$

$$ f(x) = x $$

$$ f(x) = 1 $$

$$ f(x) = 2x $$

$$ f(x) = 2x + 1 $$

$$ f(x) = \left|2x + 1\right| $$

$$ f(x) = \left| 2x + 1 \right| - 4 $$

$$ f(x) = \left| \left| 2x + 1 \right| - 4 \right| $$

$$ f(x) = \left| \left| 2x + 1 \right| - 4 \right| - 2.5 $$

$$ f(x) = \left| \left| \left| 2x + 1 \right| - 4 \right| - 2.5 \right| $$

$$ \class{mj-blue}{f(x) = 2.5 \cdot \arctan x} $$

$$ \class{mj-green}{g(x) = x} $$

$$ \class{mj-blue}{f(x) = 2.5 \cdot \arctan x} $$ $$ \class{mj-green}{g(x) = \sin 6x} $$

$$ \class{mj-red}{f(x) + g(x)} $$

$$ \class{mj-blue}{ f(x) = 0.5 + 0.5 \cdot \cos x } $$

$$ \class{mj-blue}{ f(x) = 0.5 + 0.5 \cdot \cos ( max(-\pi, min(\pi, x))) } $$

$$ \class{mj-blue}{ f(x) = 0.5 + 0.5 \cdot \cos ( max(-\pi, min(\pi, x))) } $$ $$ \class{mj-green}{ g(x) = thing(x, t) } $$

$$ \class{mj-blue}{ f(x) = 0.5 + 0.5 \cdot \cos ( max(-\pi, min(\pi, x))) } $$ $$ \class{mj-red}{ g(x) = f(x) \cdot thing(x, t) } $$