I call this type of design a “Fibonacci spiral” because the math used for it can be related to a Fibonacci sequence. The images linked here were created using specialized VB6 code to make the tiles, and then the Custom Fibonacci Spiral Generator to generate the final images.

Fixed Ratio in Sequences and Spirals

An example of a Fibonacci sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … where each term after the second one is the sum of the two preceding terms. The ratio of each term to the previous one gradually converges to a limit of approximately 1.618 (which, incidentally, is also the Golden Mean).

At each concentric layer of a Fibonacci spiral, the ratio of a single component element to one from the next layer in is a constant, which varies according to how many radially symmetrical parts of the spiral there are. This constant is what makes the expanding sequence of layers similar to the spiral pattern generated by a Fibonacci sequence of growth.

Such spirals occur frequently in nature, for example in a Nautilus shell or the center of a sunflower. It seems that each growing layer of the organism must reproduce itself in a certain expanded version one layer out, thus guaranteeing a Fibonacci pattern.

A pattern of radial symmetry whose constituent elements progress outwards with a fixed ratio between each layer results in a logarithmic spiral. The limit function of a Fibonacci sequence proceding outwards in a radial pattern is also a logarithmic spiral; hence the similarity.

The Custom Fibonacci Spiral Generator (CFSG)

CFSG allows the creation of a Fibonacci spiral with a specified number of radial parts using repeated instances of a tile provided by the user. The appearance of the spiral may be varied by setting the parameters for clines of color and brightness to be applied as the tiles progress radially outwards.

After experimenting with the CFSG application for several years, I noticed the most interesting and aesthetically pleasing Fibonacci spirals relied for their appeal on the structure of the tiles used to make them. In the twenty years since then I have focused my efforts on devising new software for the creation of tiles, searching for the elusive pattern that would produce a design of satisfying chromatic intricacy. The process culminated in the Ornate Pattern, which was based on the design of a Baroque carpet.

Below is a representative sample of Fibonacci spirals produced from tiles that were created using these advanced techniques:

Ornate Pattern	Swirl Pattern	Damask Pattern
Flower Pattern	Celtic Knot Pattern	Medallion Pattern
Roseate Pattern	Screen Pattern	Balsam Pattern
	“Eye of God” Pattern