{"id":1984,"date":"2010-11-06T01:30:46","date_gmt":"2010-11-06T06:30:46","guid":{"rendered":"http:\/\/fredhatt.com\/blog\/?p=1984"},"modified":"2014-12-14T20:44:14","modified_gmt":"2014-12-15T01:44:14","slug":"magic-squares","status":"publish","type":"post","link":"http:\/\/fredhatt.com\/blog\/2010\/11\/06\/magic-squares\/","title":{"rendered":"Magic Squares"},"content":{"rendered":"
\"\"<\/a>

Sunset Construction Shed, 2005, photo by Fred Hatt<\/p><\/div>\n

A lot of writing about proportions and composition focuses on the golden ratio or phi<\/a>.\u00a0 Relationships based on phi appear everywhere you look in natural forms and cycles.\u00a0 Artists, architects and designers frequently use the golden rectangle<\/a> based on this ratio, and it’s often considered the most beautiful of all rectangles.\u00a0 But it could be argued that the square is an even more harmonious quadrangular shape, and its perfect evenness has very special compositional qualities.<\/p>\n

The 6 x 6 cm square film format became popular for magazine photography partly because square images could be cropped to either vertical or horizontal rectangles by the editor, but photographers often found that the square frame facilitated particularly bold arrangements of their subject matter.\u00a0 Designers discovered the special qualities of the square frame in creating sleeves for LP records<\/a>, leading to some of the most iconic graphic designs of the last century.<\/p>\n

Here I share a selection of my images of New York City from the past decade, selected as examples of square compositions.\u00a0 I don’t have a square format camera, but I find that many of my photographs are improved by cropping, and the square crop is one I frequently consider.\u00a0 A criterion for choosing images for this post is that I don’t think any of these images would work as well with a vertical or horizontal frame.<\/p>\n

The top photo in this post is a perspective through the roughly square corridor of a construction shed.\u00a0 The setting sun casts long diagonal shadows of the scaffold columns, and those diagonals are countered by the thicker shape of an inclined tree trunk.\u00a0 The square frame really highlights the contrast of vertical, horizontal, and diagonal lines.\u00a0 Here’s another example:<\/p>\n

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Oblique Light, 2006, photo by Fred Hatt<\/p><\/div>\n

A square crop can break down a unified design into an arrangement of shapes and lines.<\/p>\n

\"\"<\/a>

Automotive Shapes, 2006, photo by Fred Hatt<\/p><\/div>\n

A beautiful three dimensional shape, compressed into two dimensions and framed in a square, becomes somehow even more abstractly sensuous.<\/p>\n

\"\"<\/a>

Steel Helix, 2005, photo by Fred Hatt<\/p><\/div>\n

This classic bit of architecture (The Enid A. Haupt Conservatory<\/a> at the New York Botanical Garden in the Bronx) is designed with golden ratio proportions, but a square frame really flatters it:<\/p>\n

\"\"<\/a>

White Dome, 2004, photo by Fred Hatt<\/p><\/div>\n

This view from a Brooklyn rooftop shows the special properties of the square picture.\u00a0 A wide image would be a panorama, focused on the horizon, and a tall image would emphasize the height of the vantage point.\u00a0 The square equalizes the vertical and the horizontal, and thus shows height and depth in equilibrium.<\/p>\n

\"\"<\/a>

Brooklyn Crepuscule, 2005, photo by Fred Hatt<\/p><\/div>\n

In a square frame, what is centered is idealized and what is off center is dynamic.<\/p>\n

\"\"<\/a>

Heaven and Earth, 2009, photo by Fred Hatt<\/p><\/div>\n

Straight lines and organic forms complement each other in perfect tension within the square.<\/p>\n

\"\"<\/a>

Diagonals, 2005, photo by Fred Hatt<\/p><\/div>\n

Dark and light, rounded and rectangular, perpendicular and angular: Simple polarities of form spring into relief in the balanced space of the square frame.<\/p>\n

\"\"<\/a>

Urban Sundown, 2006, photo by Fred Hatt<\/p><\/div>\n

Straight lines make quadrilaterals and triangles within the square, and curved forms break the rigidity.<\/p>\n

\"\"<\/a>

Street Fair Decorations, 2010, photo by Fred Hatt<\/p><\/div>\n

The simplest contrasts reveal their full complexity in the square.<\/p>\n

\"\"<\/a>

Piece of Gold, 2004, photo by Fred Hatt<\/p><\/div>\n

The perfect regularity and abstraction of the square can be an ideal frame for the fractal chaos of natural forms.\u00a0 Any other rectangle partakes of a bit of chaos itself, but a square remains rigorously neutral.<\/p>\n

\"\"<\/a>

Rainy Berries, 2005, photo by Fred Hatt<\/p><\/div>\n

The square’s geometrical balance can also highlight the gestural quality of a figure or sculpture.<\/p>\n

\"\"<\/a>

Command, 2006, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Sculptural Hands, 2005, photo by Fred Hatt<\/p><\/div>\n

The converging lines of perspective take on a special quality in a square frame, where verticals, horizontals, and\u00a0 diagonals exist in egalitarian relationship.<\/p>\n

\"\"<\/a>

Subway Perspective, 2004, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Fence Growth, 2007, photo by Fred Hatt<\/p><\/div>\n

Perspective compositions are made even more interesting by the addition of curves or random angles.<\/p>\n

\"\"<\/a>

Cast Iron, 2005, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Barriers, 2005, photo by Fred Hatt<\/p><\/div>\n

The elements of a square picture rest in balanced relation to all their companion elements.<\/p>\n

\"\"<\/a>

Flushing Meadows Globe, 2004, photo by Fred Hatt<\/p><\/div>\n

Perfect symmetry is actually heightened by slight elements of asymmetry.\u00a0\u00a0 The harmonious square frame magnifies both qualities.<\/p>\n

\"\"<\/a>

Church Garden, 2005, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Stone Yard, 2010, photo by Fred Hatt<\/p><\/div>\n

A square is naturally divided into rectangles and other shapes, a la Mondrian.<\/p>\n

\"\"<\/a>

Drawer Pull Display, 2006, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Eighth Avenue, 2004, photo by Fred Hatt<\/p><\/div>\n

Leaning or angular shapes have a certain natural dynamism based on their contrast with rectilinear forms.\u00a0 The square composition gives these shapes their full measure of potential energy.<\/p>\n

\"\"<\/a>

Angular Structure, 2006, photo by Fred Hatt<\/p><\/div>\n

In a square image, a living element can be a point of active concentration, seen off center in relation to a more abstract, more chaotic space, illustrating the tension inherent in the relation of the living being to the natural world.<\/p>\n

\"\"<\/a>

Fountain Joy, 2006, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Snow Mound, 2005, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Wet Asphalt, 2004, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Plywood's Red Glare, 2004, photo by Fred Hatt<\/p><\/div>\n

Expressions of style can be abstracted from their complex personal and cultural manifestations, to be observed in their purely formal aspects.<\/p>\n

\"\"<\/a>

Mosaic, 2005, , photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Instruments and Shoes, 2004, photo by Fred Hatt<\/p><\/div>\n

Just as fractal mathematics shows the rational order underlying complexity, the square frame in photography puts the unbalanced world, snarled, tangled and scattered, into a context of perfect equilibrium, illuminating the logic of chaos.<\/p>\n

\"\"<\/a>

Linear Arrangement in Streetlight, 2007, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Composition in Gray, 2004, photo by Fred Hatt<\/p><\/div>\n

\"\"<\/a>

Spilt, 2006, photo by Fred Hatt<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"

A lot of writing about proportions and composition focuses on the golden ratio or phi.\u00a0 Relationships based on phi appear everywhere you look in natural forms and cycles.\u00a0 Artists, architects and designers frequently use the golden rectangle based on this ratio, and it’s often considered the most beautiful of all rectangles.\u00a0 But it could be […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[189],"tags":[61,82,29,28,22,27],"class_list":["post-1984","post","type-post","status-publish","format-standard","hentry","category-photography-framing","tag-nature","tag-nyc","tag-seasons","tag-snapshots","tag-technique","tag-urban-landscape"],"yoast_head":"\nMagic Squares - DRAWING LIFE by fred hatt<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"http:\/\/fredhatt.com\/blog\/2010\/11\/06\/magic-squares\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Magic Squares - DRAWING LIFE by fred hatt\" \/>\n<meta property=\"og:description\" content=\"A lot of writing about proportions and composition focuses on the golden ratio or phi.\u00a0 Relationships based on phi appear everywhere you look in natural forms and cycles.\u00a0 Artists, architects and designers frequently use the golden rectangle based on this ratio, and it’s often considered the most beautiful of all rectangles.\u00a0 But it could be […]\" \/>\n<meta property=\"og:url\" content=\"http:\/\/fredhatt.com\/blog\/2010\/11\/06\/magic-squares\/\" \/>\n<meta property=\"og:site_name\" content=\"DRAWING LIFE by fred hatt\" \/>\n<meta property=\"article:published_time\" content=\"2010-11-06T06:30:46+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2014-12-15T01:44:14+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/fredhatt.com\/blog\/wp-content\/uploads\/2010\/11\/fredhatt-2005-sunset-construction-shed.jpg\" \/>\n<meta name=\"author\" content=\"fred\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"fred\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\\\/\\\/fredhatt.com\\\/blog\\\/2010\\\/11\\\/06\\\/magic-squares\\\/#article\",\"isPartOf\":{\"@id\":\"http:\\\/\\\/fredhatt.com\\\/blog\\\/2010\\\/11\\\/06\\\/magic-squares\\\/\"},\"author\":{\"name\":\"fred\",\"@id\":\"http:\\\/\\\/fredhatt.com\\\/blog\\\/#\\\/schema\\\/person\\\/c298e6b4be9e8bbc43ff45acb35fcc76\"},\"headline\":\"Magic Squares\",\"datePublished\":\"2010-11-06T06:30:46+00:00\",\"dateModified\":\"2014-12-15T01:44:14+00:00\",\"mainEntityOfPage\":{\"@id\":\"http:\\\/\\\/fredhatt.com\\\/blog\\\/2010\\\/11\\\/06\\\/magic-squares\\\/\"},\"wordCount\":1211,\"commentCount\":4,\"image\":{\"@id\":\"http:\\\/\\\/fredhatt.com\\\/blog\\\/2010\\\/11\\\/06\\\/magic-squares\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/fredhatt.com\\\/blog\\\/wp-content\\\/uploads\\\/2010\\\/11\\\/fredhatt-2005-sunset-construction-shed.jpg\",\"keywords\":[\"Nature\",\"NYC\",\"Seasons\",\"Snapshots\",\"Technique\",\"Urban Landscape\"],\"articleSection\":[\"Photography: Framing\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"http:\\\/\\\/fredhatt.com\\\/blog\\\/2010\\\/11\\\/06\\\/magic-squares\\\/\",\"url\":\"http:\\\/\\\/fredhatt.com\\\/blog\\\/2010\\\/11\\\/06\\\/magic-squares\\\/\",\"name\":\"Magic Squares - 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