Perlin Noise

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Perlin Noise

• References 1, 2

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Introduction

• Many people have used random number generators in
  their programs to create unpredictability, making
  the motion and behavior of objects appear more
  natural
• But at times their output can be too harsh to
  appear natural.
• The Perlin noise function recreates this by
  simply adding up noisy functions at a range of
  different scales.

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Noise Functions

• A noise function is essentially a seeded random
  number generator.
• It takes an integer as a parameter (seed), and
  returns a random number based on that parameter.

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Example
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Amplitude Frequency

• The red spots indicate the random values defined
  along the dimension of the function.
• frequency is defined to be 1/wavelength.

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Creating the Perlin Noise Function

• Take lots of such smooth functions, with various
  frequencies and amplitudes
• Idea similar to fractal, Fourier series,
• Add them all together to create a nice noisy
  function.

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Fractal Geometry (Koch)
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Fractal Geometry (Mandelbrot set)
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Fractal (Romanesco broccoli)
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Fourier Analysis
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Example
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Example (cont)

• Function has large, medium and small variations.

Similar to the ideas of fractal
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Alternate formula
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2 dimensions
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Persistence

• You can create Perlin noise functions with
  different characteristics by using other
  frequencies and amplitudes at each step.

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Interpolation

• Linear Interpolation
• Cosine Interpolation

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Interpolation

• Cubic Interpolation

See reference for more details
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Smoothed Noise
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Applications of Perlin Noise

• 1 dimensional
• Controlling virtual beings, drawing sketched
  lines
• 2 dimensional
• Landscapes, clouds, generating textures
• 3 dimensional
• 3D clouds, solid textures