Visual Music
Generative Patterns and Tiling
What are patterns?
A pattern is a regularity in the world, human-made design, or abstract ideas where the elements repeat in a predictable manner.
There are many different types of patterns such as:
Types of Patterns: Symmetries
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement")in everyday language refers to a sense of harmonious and beautiful proportion and balance.
In mathematics, "symmetry" has a more precise definition, that an object is invariant to any of various transformations; including reflection, rotation or scaling.
Snowflakes, such as the one pictured to the right, are an example of an object in nature that has symmetric qualities.
Types of Patterns: Spirals
Spiral patterns are found in the body plans of animals including molluscs such as the nautilus, and in the phyllotaxis of many plants, both of leaves spiralling around stems, and in the multiple spirals found in flowerheads such as the sunflower and fruit structures like the pineapple.
In mathematics spirals are defined as a curve on a plane that winds around a fixed center point at a continuously increasing or decreasing distance from the point.
Types of Patterns: Waves and Dunes
Waves are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it oscillate as they pass by. Wind waves are surface waves that create the chaotic patterns of the sea. As they pass over sand, such waves create patterns of ripples; similarly, as the wind passes over sand, it creates patterns of dunes.
Types of Patterns: Bubbles and Foam
Foam and bubble patterns occur widely in nature, for example in radiolarians, sponge spicules, and the skeletons of silicoflagellates and sea urchins.
Foams obey Plateau's laws, which require films to be smooth and continuous, and to have a constant average curvature.
Types of Patterns: Spots and Stripes
A stripe is a line or band that differs in color or tone from an adjacent area. Stripes are a group of such lines.
A spot is a circle or semi-circle that differs in color or tone from an adjacent area. Spots are a group of such circles.
In nature, spots and stripes are a mechanism that spontaneously creates patterns, for example in the skin of mammals or the plumage of birds.
Types of Patterns: Cracks
A crack is a break, or fissure, in a physical object due to stress.
Cracks form in materials to relieve stress: with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials. As such the pattern of cracks indicates whether the material is elastic or not. Cracking patterns are widespread in nature, for example in rocks, mud, tree bark and the glazes of old paintings and ceramics.
Types of Patterns: Tilings
In visual art, pattern consists in regularity which in some way "organizes surfaces or structures in a consistent, regular manner." At its simplest, a pattern in art may be a geometric or other repeating shape in a painting, drawing, tapestry, ceramic tiling or carpet, but a pattern need not necessarily repeat exactly as long as it provides some form or organizing "skeleton" in the artwork.
In mathematics, a tessellation is the tiling of a plane using one or more geometric shapes (which mathematicians call tiles), with no overlaps and no gaps.
Types of Patterns: Fractals
Fractals are mathematical patterns that are scale invariant – this means that the shape of the pattern does not depend on how closely you look at it. Self-similarity is found in fractals.
Examples of natural fractals are coast lines and tree shapes, which repeat their shape regardless of what magnification you view at.
Types of Patterns: Motifs
In architecture and visual design, an element of an image, or a motif, can be repeated in various ways to form patterns.
Most simply, structures such as windows can be repeated horizontally and vertically (see leading picture). Architects and designers can use and repeat decorative and structural elements such as columns, pediments, and lintels. Repetitions need not be identical; for example, elements of the motif pattern can repeat in a fractal-like way at different sizes.
Types of Patterns: Kaleidoscope
A kaleidoscope is an optical instrument with two or more reflecting surfaces tilted to each other in an angle, so that one or more objects on one end of the mirrors are seen as a regular symmetrical pattern when viewed from the other end, due to repeated reflection. The reflectors (or mirrors) are usually enclosed in a tube, often containing on one end a cell with loose, colored pieces of glass or other transparent (and/or opaque) materials to be reflected into the viewed pattern. Rotation of the cell causes motion of the materials, resulting in an ever-changing view being presented.
The kaleidoscope effect is often recreated digitally by image and video editing softwares.
Patterns and Gestalt Principles
Going back to our Gestalt principles, when developing patterns we can see the laws of similarity and proximity at work to create “unified wholes”
Similarity occurs when objects look similar to one another, often using translations of size, position, rotation and other distortions, while keeping properties of the original shape intact.
Proximity occurs when elements are placed close together. They tend to be perceived as a group.
With some patterns, such as spirals and fractals, we can also observe the principles of closure and continuation at work.
Types of Symmetry
A geometric shape or object is symmetric if it can be divided into two or more identical pieces that are arranged in an organized fashion. The type of symmetry is determined by the way the pieces are organized. Some types of symmetries include:
Reflective Symmetry
Pictured here are three examples of reflective symmetry, where the object is the same when mirrored along one of the drawn axis lines.
Some of these shapes, such as the square, also demonstration other symmetries such as rotational.
The fourth shape is an example of an asymmetric object.
Tiling Effects
One of the common ways to create patterns in graphics and video software is to use tiling effects.
The tile effect filters will create dramatically different results depending on the parameters of the filter, and the image being processed.
To the right, a rectangle processed with Sixfold, Eightfold and Op-Tile effects.
Patterns and Music
Music and sound often also contains patterns of different types that are similar to some of the variations of patterns we have discussed in visuals. When creating visual music, we can also consider how these concepts can be translated from sound to vision:
Demonstrations