The story
A halo around the moon forms when light refracts through ice crystals in high clouds, always at an angle of 22°. Here only 15 rings, the fewest in the series, and three envelopes.
Fine art paper
200 gsm enhanced matte
Printed on thick uncoated art paper at 300 DPI. Rich colour, razor-sharp lines, no glare.
Real wood frames
Black or natural wood
Wooden frame, 22 mm deep, with plexiglass that is lighter and safer than glass. Arrives ready to hang.
Made to order
Free shipping worldwide
Each print is made for you when you order and packed to arrive flawless, wherever you are.
MATHEMATICS
The maths behind the picture
Every piece is computed, not drawn. These are the real equations and numbers from the program that made this exact piece.
Read the guide: Perlin noise explained →Equations
rᵢ(θ) = Rᵢ + A·env(θ)·eᵢ·(1.56·n₁(θ)² + 0.45·|sin(f·θ + φᵢ)|³·n₂(θ))env(θ) = Σₖ aₖ·e^(−(Δ(θ, cₖ)/wₖ)²)
Parameters
- Rings
- 15
- Carrier frequency
- 48
- Envelopes
- 263.6°±15.6° · 257.9°±17.7° · 79.5°±12.3°
- Perlin noise
- 4 octaves · falloff 0.5
Measured while drawing
- Samples
- 13,500
What these numbers mean
Nature is neither perfectly smooth nor completely random: clouds, mountains and waves are somewhere in between. In 1983 Ken Perlin invented a noise that looks like nature: a smooth function that gives random but gentle changes. The program adds four layers (octaves) of this noise, each half as strong and twice as fine as the last. That is what gives the lines life, so they don't look like they were drawn with a ruler.
HISTORY
Where this idea comes from
- 1691
Jacob Bernoulli develops polar coordinates: a point is described by an angle and a distance from the centre instead of x and y.
- 1890s
Harmonographs, pendulum drawing machines, trace circular wave patterns and become a popular Victorian art.
- 1983
Perlin noise, sampled around a circle, makes seamless rings that close perfectly through all 360°.
Perlin noise
- 1982
Ken Perlin works on the effects for the film Tron and is frustrated that computer images look too "machine-like".
- 1983
Perlin invents his noise and publishes it in 1985 at SIGGRAPH, in the paper "An Image Synthesizer".
- 1997
Perlin receives an Academy Award for Technical Achievement: his noise becomes the basis of smoke, fire and cloud textures in film.
- 2001
Perlin publishes an improved version and "simplex" noise. Today games, films and programmer art all over the world use it.
In nature
A signal wound into a circle records the way tree rings do: ring by ring, their width following drought and rain.
Follow along
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