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Introduction to Perlin Noise Perlin Noise was developed by Ken Perlin in 1983 for the film Tron as a smooth pseudo-random noise algorithm1. It can generate random patterns with natural-looking texture and is widely used in computer graphics to simulate natural phenomena such as clouds, terrain, fire, wood grain, and water flow2. Unlike plain white noise, Perlin Noise has spatial correlation: values at neighboring sample points vary smoothly without abrupt jumps. This smoothness makes the generated textures resemble the continuous variations found in nature. ...

This article focuses solely on the following topics: Transition from trigonometric series expansion to the Euler form of the Fourier transform What the Discrete Fourier Transform is What the 2D Fourier Transform is Explanation of the 2D Discrete Fourier Transform from the 2D Fourier Transform How to perform a 2D Fourier transform on an image Periodicity issues in the 2D Fourier transform Understanding the centering of the 2D frequency spectrum from the periodicity of the 2D Fourier transform Fourier Series A Fourier series is a mathematical tool that represents a periodic function as an infinite sum of sines and cosines. ...