\(
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\newcommand{\empty}[]{\emptyset}
\newcommand{\O}[]{\emptyset}
\newcommand{\Alpha}[]{Α}
\newcommand{\Beta}[]{Β}
\newcommand{\Epsilon}[]{Ε}
\newcommand{\Iota}[]{Ι}
\newcommand{\Kappa}[]{Κ}
\newcommand{\Rho}[]{Ρ}
\newcommand{\Tau}[]{Τ}
\newcommand{\Zeta}[]{Ζ}
\newcommand{\Mu}[]{\unicode{x039C}}
\newcommand{\Chi}[]{Χ}
\newcommand{\Eta}[]{\unicode{x0397}}
\newcommand{\Nu}[]{\unicode{x039D}}
\newcommand{\Omicron}[]{\unicode{x039F}}
\DeclareMathOperator{\sgn}{sgn}
\def\oiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x222F}\,}{\unicode{x222F}}{\unicode{x222F}}{\unicode{x222F}}}\,}\nolimits}
\def\oiiint{\mathop{\vcenter{\mathchoice{\huge\unicode{x2230}\,}{\unicode{x2230}}{\unicode{x2230}}{\unicode{x2230}}}\,}\nolimits}
\)
Algorithm
- Generate a grid of random unit-length vectors
- In improved perlin noise, vectors which only contain +=1 and 0 such as (1, 1, 0) are used
- For each point, find the closest corners in the grid and compute the dot product between the vector from the corner and the corner's random vector.
- Interpolate between these using smoothstep.
Resources
