Overview of PhiMatrix™
concepts and applications
Phi: Noun, fI or fee - The 21st letter of the Greek alphabet
used to represent the irrational number 1.6180339887..., or 1.618 for short.
Matrix: Noun, 'mA-triks - A surrounding substance within which something else
originates, develops, or is contained.
Whether you look to quantum mechanics or to
movies like "The Matrix," a deeper understanding of reality is unveiled once
you understand the matrix upon which it is built. The matrix upon which the
proportions of life and the universe is constructed is based on the number known
PhiMatrix is a graphic analysis and design tool that lets you
see and apply phi proportions to any image. It
overlays any other program you have on your computer, from digital image editing
software to your "My Pictures" folder, and then lets you save
your analyzed image to disk.
It's unique features include:
- Variable proportioning of the grid in height and
width that allows application of the copyrighted "Golden Ruler™"
and "Golden Grid™"
concepts to be applied to images and objects of any dimension.
Traditional golden section analysis has used a rectangle with height and width
fixed in proportion to phi, or 1.618.
- A grid mirroring feature that allows the grid lines to be independently mirrored
vertically on the left and right
sides of the grid, and horizontally on the top and bottom halves of the grid.
The grid proportions can also be locked into a user sizable golden section in
portrait or landscape orientation.
- User selection of the number of grid lines to
be shown, with independent selection options for the horizontal and vertical
- User selectable border width outside the grid,
especially useful when creating and/or cropping images to be saved to disk.
It can be used for any design application your
mind can conceive, whether laying out a canvas for painting, cropping a photo, creating marketing
materials or designing everything from clothes to cars to furniture to buildings.
While the Golden Section has been used for
centuries, the concept for PhiMatrix is based on an original insight of its
developer in 1997 that the Golden Section could be applied in repetition to a
line to create a "Golden Ruler™." Each section of the ruler is
in phi proportion to the section from which it came:
This Golden Ruler was then applied in two
dimensions to create a "Golden Grid™."
The Golden Section analysis is traditionally used with
a fixed phi proportion of 1.618 in the height and width. The "Golden
Grid" concept applied in the PhiMatrix software allows proportions to be variable in height and
width, yet still shows the "golden ruler" sections on both the horizontal and
Application of these concepts to images of a
variety of life forms revealed that their physical dimensions were all based
upon the same proportions of design using the number
Examples are shown below.
These same proportions have been used by mankind
to achieve some of its greatest works of art and architecture.
It's now being used in design for a variety of applications:
- Automotive design
- Logos and trademarks
- Cosmetic and corrective dentistry
- Reconstructive and corrective facial surgery
- Clothing design
- Hair styling
- Design, layout and composition of marketing
and advertising materials
- Photo editing and composition
- Stock market analysis
The Golden Ruler and Golden Grid were first
presented in 1997 from http://goldennumber.net
(and its predecessor site) in
the form of a template that could be printed to a transparency and used as an
overlay to documents. PhiMatrix expands this concept and capability to
About Phi and its unusual properties
Phi ( = 1.618033988749895... ), most often pronounced fi like
"fly," is simply an irrational number like pi ( p = 3.14159265358979... ), but
one with many unusual mathematical properties.
The ratio, or proportion, determined by Phi (1.618...) was known to the Greeks
as the "Golden Section" and to Renaissance artists as the "Divine Proportion" It
is also called the Golden Ratio and the Golden Mean.
Just as pi (p) is the ratio of the circumference of a circle to its diameter,
phi is simply the ratio of the line segments that result when a line is divided
in one very special and unique way.
|Divide a line so that:
|the ratio of the length of
the entire line (A)
to the length of larger line segment (B)
is the same as
the ratio of the length of the larger line segment (B)
to the length of the smaller line segment (C).
More simply, A is to B as B is to C.
This happens only at the point where A is 1.618... times B and B is 1.618...
times C. Alternatively, C is 0.618... of B and B is 0.618... of A.
Phi with an upper case "P" is 1.6180339887..., while phi with a lower case "p"
is 0.6180339887, which is the reciprocal of Phi and also Phi minus 1. Phi
is the only number whose reciprocal has a difference in value of 1. Phi
can be calculated by adding 1 to the square root of 5 and then dividing the sum
What makes phi unusual is that it can be derived in many ways mathematically and
geometrically and shows up in
relationships throughout the universe. Phi appears in the proportions of the human
body and face, the proportions of many other animals, plants, DNA, the solar system,
population growth the stock market and in many aspects of life and the universe.
Our perceptions of beauty in the humans are based on how close facial
proportions conform to phi.
Some believe phi is the most efficient outcome, the result
of natural forces. Some believe it is a universal constant of design, the
signature of God. Whatever you believe, the pervasive appearance of phi in
all we see and experience creates a sense of balance, harmony and beauty in the
design of all we find in nature. It should be no surprise then that
mankind would use this same proportion found in nature to achieve balance,
harmony and beauty in its own creations of art, architecture, colors, design,
composition, space and even music.
The Golden Section, the phi relationship, has long been used
by craftsmen and professionals of many fields to understand and achieve beauty,
balance and harmony in their work. Artists, architects, designers, engineers,
musicians, photographers, sculptors, surgeons and stock analysts alike use this
relationship to achieve excellence in their results.
The study and application of the golden section is now much
easier with PhiMatrix software. Put your ruler and calculator away and let
the phi relationships just jump out at you as you work or play with the software
to bring your work to a new level in any field.
Learn more about phi at the
http://goldennumber.net, also developed by Gary B. Meisner, the developer of