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Introduction to Spirals
Under Construction

Spirals are found on every scale through out our universe. The invention of telescopes and microscopes has given us to access to hidden worlds both under our noses and light-years away, and these worlds abound with patterns, the spiral prevalent among them.

Science: Fact & Theory
In this website you will encounter both facts and theories about spirals.

Facts are based on observation. For example, the nautilus shell expresses a logarithmic spiral. This statement can be proved mathematically. It is a fact. However, facts themselves are subject to new information and are often under dispute.

Theories are explanations that answer the questions why and how:
How do spirals grow?
Why are spirals found on every scale?
What does this mean about the fundamental properties of the universe?

The answers to these questions are theories.

Science: The Search for Fundamental Laws
Scientists look at the world and try to uncover the fundamental laws of nature: why are things the way they are?

This website presents fairly simple versions of very complex ideas, both fact and theory.

What is a Spiral? (spirals images)
As you have seen if you’ve visited any of the image galleries on this site, spirals come in all shapes and sizes. Different types of spirals have different names; some of them are illustrated below.

Here are definitions of spiral from the Oxford Dictionary:

adjective: winding in a continuous curve around a central point or axis.

noun: 1 a spiral curve, shape, or pattern. 2 a progressive rise or fall of prices, wages, etc., each responding to an upward or downward stimulus provided by a previous one. 3 a process of progressive deterioration.

verb: (spiralled, spiralling; US spiraled, spiraling) 1 take or cause to follow a spiral course. 2 show a continuous and dramatic increase or decrease.

  — ORIGIN Latin spiralis, from Greek speira ‘a coil’

Spiralzoom is primarily interested in the spiral as a pattern.

Patterns (more patterns)
As noted, the spiral is a pattern. Although humans have adopted the spiral as a cultural motif, it originated as a natural pattern—one of creation’s methods of organization.  Other commonly-occurring patterns in nature include:

Branching patterns


Explosion patterns

Patterns & Packing
One explanation for why patterns recur throughout nature is that they provide the most efficient use of materials and space. Spirals, for one, are common because they can be formed following the repetition of a few simple rules, because they can be easily expanded by those same rules, because they are stronger and more flexible than straight surfaces, and because they provide great stability and organization (think of a Slinky: when it is neatly coiled in its spiral shape, it is very compact and can slither and bounce with ease; when it is forced out of its customary spiral form, it becomes disorganized, takes up more space, and loses its ability to flow).

Science vs Technology
The Science section of this website concerns spirals that are found in the natural world.

You can see examples of inventions based on spirals in the Culture section of the website:
Engineering & Technology

But wait a minute, aren't inventions part of science? 
In this project they are classified under  "culture" because they are things that people create. 
This is a mathematical formula that means “Logarithmic Spiral.” To a mathematician, this conveys precisely the shape of the curve.
The Helix:
This spiral is like a corkscrew or phone cord.
Equiangular or
Logarithmic spiral
Each layer of the spiral gets
bigger as it grows.
Archimedian Spiral
This spiral is like a coil of rope. Each whorl is the same width.
The Link between Math & Science
Visit Xah Lee Web for great information on:
Spirals & Math

Also visit the spirals page at
Mathworld, Mathematica