Stefan Hollos - Art of the Golden Ratio

Art of the Golden Ratio
by Stefan Hollos and J. Richard Hollos
Ebook ISBN 978-1-887187-20-6

Copyright 2014, 2015 by Exstrom Laboratories LLC

All rights reserved. No part of this document may be reproduced or transmittedin any form or by any means, electronic or mechanical, including photocopying,recording, or by any information storage and retrieval system, withoutpermission in writing from the publisher.

Abrazol Publishing
an imprint of Exstrom Laboratories LLC
662 Nelson Park Drive,
Longmont, CO 80503-7674 U.S.A.

Mathematics is full of mystery and beauty. Few mathematicians would disagree with that. Most people would agree with the mystery part but not the beauty. There is however one mathematical object that has often been associated with beauty and aesthetics, at least by artists. That object is an irrational number called the golden ratio. It is believed by some that a piece of art that exhibits this ratio in some way is more aesthetically pleasing.

In a painting this could be as simple as making the ratio of the width to height equal to the golden ratio. In architecture it could mean making the dimensions of a room agree with the golden ratio. Whether these beliefs are true or not is not for us to say. Anyone wanting to explore these aesthetic ideas further can look at some of the references at the end of this book.

What we have found, and what this book is about, is the fact that the golden ratio does indeed encode many intricate patterns that can be turned into interesting drawings. We have collected 360 of these drawings together in this book. The book is an art book meant to stimulate your creativity and imagination. There is no mathematics required. We have included two appendices that contain a very short explanation of some of the mathematics behind the golden ratio and how the images are created, indexed by name. More detailed information on how to create the images can be found in our book:

Pattern Generation for Computational Art

May you find these images stimulating and inspirational, as we have found them.

Stefan Hollos and Richard Hollos
Exstrom Laboratories LLC
Longmont, Colorado

The new art must be based upon science in particular, upon mathematics, as the most exact, logical, and graphically constructive of the sciences.
Albrecht Durer

Study and in general the pursuit of truth and beauty is a sphere of activity in which we are permitted to remain children all our lives.
Albert Einstein

To be an artist you have to give up everything, including the desire to be a good artist.
Jasper Johns

The man with insight enough to admit his limitations comes nearest to perfection.
Johann Wolfgang von Goethe

Great artists are people who find the way to be themselves in their art. Any sort of pretension induces mediocrity in art and life alike.
Margot Fonteyn

The hardest battle youre ever going to fight is the battle to be just you.
Leo Buscaglia

When I think of art, I think of beauty. Beauty is the mystery of life. It is not in the eye, it is in my mind. In our minds there is awareness of perfection.
Agnes Martin, Beauty Is the Mystery of Life

Perhaps we cannot raise the winds. But each of us can put up the sail, so that when the wind comes we can catch it.
E. F. Schumacher

No great artist ever sees things as they really are. If he did, he would cease to be an artist.
Oscar Wilde

He that seeks popularity in art closes the door on his own genius: as he must needs paint for other minds, and not for his own.
Anna Jameson

An artist must find his expression closely linked to his individual experience or else follow in the old grooves resulting in lifeless forms.
Mark Tobey

At very best, a person wrapped up in himself makes a small package.
Harry Emerson Fosdick

All we have, it seems to me, is the beauty of art and nature and life, and the love which that beauty inspires.
Edward Abbey

There is no cosmetic for beauty like happiness.
Marguerite Gardiner, Countess of Blessington

Modern aesthetics is crippled by its dependence upon the concept of beauty. As if art were about beauty as science is about truth!
Susan Sontag

Religion and art spring from the same root and are close kin. Economics and art are strangers.
Willa Cather

There is only one pleasure - that of being alive. All the rest is misery.
Cesare Pavese

Every man is his own doctor of divinity, in the last resort.
Robert Louis Stevenson

You have to grow all the time, I said. Not necessarily get bigger. But inside your head you have to grow, kid-boy. For us human-type people, thats whats important. And that kind of growing never stops. At least, it shouldnt. You can grow, kid-boy, or you can die. Thats the choice youve got, and it goes on all of your life.
Samuel R. Delany

Mastering an art is like reaching the top of the passion mountain...at the top the passion dies out! So keep learning.
Siddharth Katragadda

Children wear their natures like brightly-colored clothes; thats why they lie so transparently. Adulthood is the art of deceit.
Robert Charles Wilson

All animals, except man, know that the principal business of life is to enjoy it.
Samuel Butler

How rare that an artist should make something which forces us to think, and encourages us to stop and think, to question why we behave the way we do.