The Golden Mean (Phi)

The Fibonacci sequence is a series of numbers which appear throughout nature. This sequence can be used to calculate the golden mean (or the golden section) which is represented by the Greek letter Phi. The Fibonacci sequence and Phi can be found visually in plants and seashells, and in the reproductive family trees of animals.

The sequence starts out: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and continues ad infinitum. Each new number in the sequence is created by adding the previous two numbers. For example, the sum of 8 + 13 is 21, making 21 the next number after 13.

Phi, also known as the golden mean, is the ratio between two sequential numbers in the Fibonacci sequence. When 1597 is divided by 987 the result is 1.618034447821682, which rounds to 1.618. The higher the numbers used to create the ratio, the more exact the calculation becomes.

Further study about the patterned relationships among mathematics, nature, music, and visual art can be found in Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter.

Self-similarity

There is a special kind of pattern that is self-similar, meaning the building unit contained in the pattern is the same as the overall completed shape. Cultural patterns often use self-similarity to suggest infinity and visually express other philosophical and existential concepts.

Fractals

A fractal is a shape that is self-similar and has a fractional dimension. Self-similarity is a required element in fractals, but all self-similar shapes are not fractals. With fractals, an infinite number of self-similar shapes can be found inside a larger shape, or the shape used as the pattern’s building unit can be “grown” into infinite detail by using itself as the blueprint. Each of these stages with smaller divisions is called an iteration.

Applying Pattern

Pattern is an extremely powerful method to focus viewer attention. The repetition easily seen in most patterns uses all of the Gestalt principles discussed in previous articles. For that reason, pattern is often used in design as a tool for organization, especially when used with text. Common methods for pattern-based organization include:

• Bullets and other shapes to list, outline, and highlight
• Alternating row colors to make individual items stand out, yet still be part of a whole
• Grid-based layout where similar shapes create a common theme, even if the content within the shapes is dissimilar (for example, different photos that are all cropped to the same size and shape and arranged in a grid pattern)
• Color-coding

Because of the power of pattern as a visual element, it is important to use it for desired effect. A pattern can unintentionally destroy the intended message of a visual work by competing with other elements. Even if a pattern is decorative it still must be considered as part of the whole composition as with other complex shapes.

Tiled backgrounds can become distracting and make the other content more difficult to follow because the viewer is naturally drawn to the repetition of the pattern.

Patterns that use grids face another problem. An optical illusion can be created by high contrast areas. This is due to the way the human retina works, and the only true method for avoiding this problem is to change the pattern itself.

Moiré patterns occur when patterns of different frequencies are used together. This can be easily observed when halftoned images are reproduced using another patterned technology. For example, the halftone printed images from a magazine are already arranged in a pattern that is a different frequency from the pixels created by a scanner and the pixels displayed on a computer monitor. Moiré patterns are also created when striped or checkered patterns appear on video. A solution that sometimes works for scanning is to scan at the highest quality possible and drastically reduce the size using photo software. Applying a Gaussian blur to the image before it is reduced sometimes helps as well, but there is no exact method because each image is different and may be printed at a different halftone screen frequency.

The solution for Moiré patterns in video is simple: don’t wear fine stripes or fine checkered patterns when you’re going to appear on television.

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Use of pattern can add interest as well as visual information to your project. Patterns can be used to enhance many purely figurative designs, as well as decoratively to complement text. Pattern is a strong visual tool that should not be overlooked.