Redalyc.Personal Reflections on Jackson Pollock's Fractal Paintings
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Fractal Expressionism—Where Art Meets Science
Santa Fe Institute. February 14, 2002 9:04 a.m. Taylor page 1 Fractal Expressionism—Where Art Meets Science Richard Taylor 1 INTRODUCTION If the Jackson Pollock story (1912–1956) hadn’t happened, Hollywood would have invented it any way! In a drunken, suicidal state on a stormy night in March 1952, the notorious Abstract Expressionist painter laid down the foundations of his masterpiece Blue Poles: Number 11, 1952 by rolling a large canvas across the oor of his windswept barn and dripping household paint from an old can with a wooden stick. The event represented the climax of a remarkable decade for Pollock, during which he generated a vast body of distinct art work commonly referred to as the “drip and splash” technique. In contrast to the broken lines painted by conventional brush contact with the canvas surface, Pollock poured a constant stream of paint onto his horizontal canvases to produce uniquely contin- uous trajectories. These deceptively simple acts fuelled unprecedented controversy and polarized public opinion around the world. Was this primitive painting style driven by raw genius or was he simply a drunk who mocked artistic traditions? Twenty years later, the Australian government rekindled the controversy by pur- chasing the painting for a spectacular two million (U.S.) dollars. In the history of Western art, only works by Rembrandt, Velazquez, and da Vinci had com- manded more “respect” in the art market. Today, Pollock’s brash and energetic works continue to grab attention, as witnessed by the success of the recent retro- spectives during 1998–1999 (at New York’s Museum of Modern Art and London’s Tate Gallery) where prices of forty million dollars were discussed for Blue Poles: Number 11, 1952. -
De Divino Errore ‘De Divina Proportione’ Was Written by Luca Pacioli and Illustrated by Leonardo Da Vinci
De Divino Errore ‘De Divina Proportione’ was written by Luca Pacioli and illustrated by Leonardo da Vinci. It was one of the most widely read mathematical books. Unfortunately, a strongly emphasized statement in the book claims six summits of pyramids of the stellated icosidodecahedron lay in one plane. This is not so, and yet even extensively annotated editions of this book never noticed this error. Dutchmen Jos Janssens and Rinus Roelofs did so, 500 years later. Fig. 1: About this illustration of Leonardo da Vinci for the Milanese version of the ‘De Divina Proportione’, Pacioli erroneously wrote that the red and green dots lay in a plane. The book ‘De Divina Proportione’, or ‘On the Divine Ratio’, was written by the Franciscan Fra Luca Bartolomeo de Pacioli (1445-1517). His name is sometimes written Paciolo or Paccioli because Italian was not a uniform language in his days, when, moreover, Italy was not a country yet. Labeling Pacioli as a Tuscan, because of his birthplace of Borgo San Sepolcro, may be more correct, but he also studied in Venice and Rome, and spent much of his life in Perugia and Milan. In service of Duke and patron Ludovico Sforza, he would write his masterpiece, in 1497 (although it is more correct to say the work was written between 1496 and 1498, because it contains several parts). It was not his first opus, because in 1494 his ‘Summa de arithmetic, geometrica, proportioni et proportionalita’ had appeared; the ‘Summa’ and ‘Divina’ were not his only books, but surely the most famous ones. For hundreds of years the books were among the most widely read mathematical bestsellers, their fame being only surpassed by the ‘Elements’ of Euclid. -
Jackson Pollock & Tony Smith Sculpture
Jackson Pollock & Tony Smith Sculpture An exhibition on the centennial of their births MATTHEW MARKS GALLERY Jackson Pollock & Tony Smith Speculations in Form Eileen Costello In the summer of 1956, Jackson Pollock was in the final descent of a downward spiral. Depression and alcoholism had tormented him for the greater part of his life, but after a period of relative sobriety, he was drinking heavily again. His famously intolerable behavior when drunk had alienated both friends and colleagues, and his marriage to Lee Krasner had begun to deteriorate. Frustrated with Betty Parsons’s intermittent ability to sell his paintings, he had left her in 1952 for Sidney Janis, believing that Janis would prove a better salesperson. Still, he and Krasner continued to struggle financially. His physical health was also beginning to decline. He had recently survived several drunk- driving accidents, and in June of 1954 he broke his ankle while roughhousing with Willem de Kooning. Eight months later, he broke it again. The fracture was painful and left him immobilized for months. In 1947, with the debut of his classic drip-pour paintings, Pollock had changed the direction of Western painting, and he quickly gained international praise and recog- nition. Four years later, critics expressed great disappointment with his black-and-white series, in which he reintroduced figuration. The work he produced in 1953 was thought to be inconsistent and without focus. For some, it appeared that Pollock had reached a point of physical and creative exhaustion. He painted little between 1954 and ’55, and by the summer of ’56 his artistic productivity had virtually ground to a halt. -
Simple Rules for Incorporating Design Art Into Penrose and Fractal Tiles
Bridges 2012: Mathematics, Music, Art, Architecture, Culture Simple Rules for Incorporating Design Art into Penrose and Fractal Tiles San Le SLFFEA.com [email protected] Abstract Incorporating designs into the tiles that form tessellations presents an interesting challenge for artists. Creating a viable M.C. Escher-like image that works esthetically as well as functionally requires resolving incongruencies at a tile’s edge while constrained by its shape. Escher was the most well known practitioner in this style of mathematical visualization, but there are significant mathematical objects to which he never applied his artistry including Penrose Tilings and fractals. In this paper, we show that the rules of creating a traditional tile extend to these objects as well. To illustrate the versatility of tiling art, images were created with multiple figures and negative space leading to patterns distinct from the work of others. 1 1 Introduction M.C. Escher was the most prominent artist working with tessellations and space filling. Forty years after his death, his creations are still foremost in people’s minds in the field of tiling art. One of the reasons Escher continues to hold such a monopoly in this specialty are the unique challenges that come with creating Escher type designs inside a tessellation[15]. When an image is drawn into a tile and extends to the tile’s edge, it introduces incongruencies which are resolved by continuously aligning and refining the image. This is particularly true when the image consists of the lizards, fish, angels, etc. which populated Escher’s tilings because they do not have the 4-fold rotational symmetry that would make it possible to arbitrarily rotate the image ± 90, 180 degrees and have all the pieces fit[9]. -
Secondary School Worksheet
Secondary school worksheet Abstract Expressionism National Gallery of Australia, Canberra International Galleries: 14 July 2012–24 February 2013, Orde Poynton Gallery: 4 August 2012–20 January 2013 Abstract Expressionism is an art movement that dominated the international art world after World War II. It emphasised spontaneity, intuition and the physical act of painting. This set it apart from earlier abstract art, which had a stricter geometric basis. Although the term Abstract Expressionism encompasses several different styles and techniques, some common features of this approach include the prominence of dramatic scale, colour and texture; a visible emphasis on the dripping, scraping and brushing of paint; and the radical simplification of the image. The artists were also seen as socially rebellious, sharing a strong belief in the value of individual creative freedom. In the history of art, Abstract Expressionism marks a shift in focus from Paris to New York as a global centre for cultural production. Its influence also spread to Australia, where it shaped the work of a generation of abstract artists. The works in the exhibition are drawn from the permanent collection of the National Gallery of Australia, with the addition of two loans from the National Gallery of Victoria, Melbourne, and one from the Art Gallery of New South Wales, Sydney. Jackson Pollock Blue poles 1952 oil, enamel, aluminium paint, glass on canvas 212.1 x 488.9 cm National Gallery of Australia, Canberra, purchased 1973 © Pollock/Krasner Foundation/ARS. Licensed by Viscopy Abstract Expressionism is a style renowned for gestural expression and the creative role of chance. As always, however, artistic forethought played a part in the work of artists such as Jackson Pollock. -
Leonardo Universal
Leonardo Universal DE DIVINA PROPORTIONE Pacioli, legendary mathematician, introduced the linear perspective and the mixture of colors, representing the human body and its proportions and extrapolating this knowledge to architecture. Luca Pacioli demonstrating one of Euclid’s theorems (Jacobo de’Barbari, 1495) D e Divina Proportione is a holy expression commonly outstanding work and icon of the Italian Renaissance. used in the past to refer to what we nowadays call Leonardo, who was deeply interested in nature and art the golden section, which is the mathematic module mathematics, worked with Pacioli, the author of the through which any amount can be divided in two text, and was a determined spreader of perspectives uneven parts, so that the ratio between the smallest and proportions, including Phi in many of his works, part and the largest one is the same as that between such as The Last Supper, created at the same time as the largest and the full amount. It is divine for its the illustrations of the present manuscript, the Mona being unique, and triune, as it links three elements. Lisa, whose face hides a perfect golden rectangle and The fusion of art and science, and the completion of the Uomo Vitruviano, a deep study on the human 60 full-page illustrations by the preeminent genius figure where da Vinci proves that all the main body of the time, Leonardo da Vinci, make it the most parts were related to the golden ratio. Luca Pacioli credits that Leonardo da Vinci made the illustrations of the geometric bodies with quill, ink and watercolor. -
Leonardo Da Vinci's Study of Light and Optics: a Synthesis of Fields in The
Bitler Leonardo da Vinci’s Study of Light and Optics Leonardo da Vinci’s Study of Light and Optics: A Synthesis of Fields in The Last Supper Nicole Bitler Stanford University Leonardo da Vinci’s Milanese observations of optics and astronomy complicated his understanding of light. Though these complications forced him to reject “tidy” interpretations of light and optics, they ultimately allowed him to excel in the portrayal of reflection, shadow, and luminescence (Kemp, 2006). Leonardo da Vinci’s The Last Supper demonstrates this careful study of light and the relation of light to perspective. In the work, da Vinci delved into the complications of optics and reflections, and its renown guided the artistic study of light by subsequent masters. From da Vinci’s personal manuscripts, accounts from his contemporaries, and present-day art historians, the iterative relationship between Leonardo da Vinci’s study of light and study of optics becomes apparent, as well as how his study of the two fields manifested in his paintings. Upon commencement of courtly service in Milan, da Vinci immersed himself in a range of scholarly pursuits. Da Vinci’s artistic and mathematical interest in perspective led him to the study of optics. Initially, da Vinci “accepted the ancient (and specifically Platonic) idea that the eye functioned by emitting a special type of visual ray” (Kemp, 2006, p. 114). In his early musings on the topic, da Vinci reiterated this notion, stating in his notebooks that, “the eye transmits through the atmosphere its own image to all the objects that are in front of it and receives them into itself” (Suh, 2005, p. -
Ben Heller, Pioneering Collector of Abstract Expressionism: ‘There’S Nobody Else in That League’
Est. 1902 home • ar tnews • news Ben Heller, Pioneering Collector of Abstract Expressionism: ‘There’s Nobody Else in That League’ BY MAXIMILÍANO DURÓN March 3, 2021 11:00am Jackson Pollock paintings are returned to Ben Heller's Central Park West apartment in New York in April 1959. MUSEUM OF MODERN ART, NEW YORK/LICENSED BY SCALA/ART RESOURCE, NEW YORK Ben Heller (https://www.artnews.com/t/ben-heller/), who died in 2019, amassed a legendary collection of Abstract Expressionism, supporting artists like Jackson Pollock, Mark Rothko, and others at a time when few else would. But before he dispersed his works to some of the world’s top museums, in particular the Museum of Modern Art (https://www.artnews.com/t/museum-of-modern-art/) in New York, he kept them in his Central Park West apartment. Thousands of visitors made the pilgrimage each year to his home to see masterpieces by the likes of Pollock, Rothko, Franz Kline, and Barnett Newman, with Rothko even referring to Heller’s apartment as “the Frick of the West Side.” When he began seriously collecting Abstract Expressionism during the ’50s, museums like MoMA largely ignored the movement. Heller rushed in headlong. “He wasn’t someone to say, ‘Let me take a gamble on this small picture so that I don’t really commit myself.’ He committed himself a thousand percent, which is what he believed the artists were doing,” Ann Temkin, chief curator of painting and sculpture at MoMA, said in an interview. Though Heller was never formally a board member at MoMA—“I was neither WASP-y enough nor wealthy enough,” he once recalled—he transformed the museum, all the while maintaining close relationships with artists and curators in its circle. -
FOR IMMEDIATE RELEASE August 18, 2015
FOR IMMEDIATE RELEASE August 18, 2015 MEDIA CONTACT Emily Kowalski | (919) 664-6795 | [email protected] North Carolina Museum of Art Presents M. C. Escher, Leonardo da Vinci Exhibitions and Related Events Raleigh, N.C.—The North Carolina Museum of Art (NCMA) presents two exhibitions opening in October 2015: The Worlds of M. C. Escher: Nature, Science, and Imagination and Leonardo da Vinci’s Codex Leicester and the Creative Mind. The Worlds of M. C. Escher features over 130 works (some never before exhibited) and will be the most comprehensive Escher exhibition ever presented in the United States. The Codex Leicester is a 500-year-old notebook handwritten and illustrated by inventor, scientist, and artist Leonardo da Vinci—the only manuscript by Leonardo in North America—that offers a glimpse into one of the greatest minds in history. “This is going to be an exciting fall at the Museum—an incredibly rare opportunity for our visitors to see not only centuries-old writings and sketches by Leonardo da Vinci, but also the work of M. C. Escher, another observer of nature and a perfect modern counterpart to Leonardo,” says NCMA Director Lawrence J. Wheeler. “These exhibitions will thrill art lovers and science lovers alike, and we hope that all visitors leave with a piqued curiosity, an ignited imagination, and a desire to more closely observe the world around them.” The Worlds of M. C. Escher: Nature, Science, and Imagination October 17, 2015−January 17, 2016 Comprising over 130 woodcuts, lithographs, wood engravings, and mezzotints, as well as numerous drawings, watercolors, wood blocks, and lithographic stones never before exhibited, The Worlds of M. -
Tessellations Hardscape Creations Inspired by the Works of M.C
Tessellations Hardscape Creations Inspired by the works of M.C. Escher © Chris Belthoff CSB Enterprises, 2013 December 2013 Proprietary 1 Contents Origin What inspired the efforts to produce my hardscape designs Construction How I created the first examples of pavers based on the designs December 2013 2 The Inspiration Ever since I was a child I’ve been fascinated by mathematics In particular, I was always interested in symmetry and patterns…. © Chris Belthoff Enterprises, 2013 December 2013 Proprietary 3 Symmetry and Patterns Have Existed Since Before Man Nature exhibits them all the time: © Chris Belthoff Enterprises, 2013 December 2013 Proprietary 4 ….and Humans Have Creatively Employed Symmetry and Patterns for Centuries © Chris Belthoff Enterprises, 2013 December 2013 Proprietary 5 So what is ‘Tessellation’ A tessellation is the tiling of a plane using one or more geometric shapes, with no overlaps and no gaps Tessellation or tiling is the branch of mathematics that studies how shapes, known as tiles, can be arranged to fill a plane without any gaps. More formally: a tessellation or tiling is a partition of the Euclidean plane into a countable number of closed sets called tiles, such that the tiles intersect only on their boundaries. These tiles may be polygons or any other shapes. Many tessellations are formed from a finite number of prototiles; all tiles in the tessellation are congruent to one of the given prototiles. If a geometric shape can be used as a prototile to create a tessellation, the shape is said to be able to tessellate or to “tile the plane”. Mathematicians have found no general rule for determining if a given shape can tile the plane or not, which means there are many unsolved problems concerning tessellations. -
How a Mathematician Started Making Movies 185
statements pioneers and pathbreakers How a Mathematician Started Making Movies M i ch e l e e M M e R The author’s father, Luciano Emmer, was an Italian filmmaker who made essentially two—possibly three—reasons. The first: In 1976 I feature movies and documentaries on art from the 1930s through was at the University of Trento in northern Italy. I was work- 2008, one year before his death. Although the author’s interest in films ing in an area called the calculus of variations, in particular, inspired him to write many books and articles on cinema, he knew he ABSTRACT would be a mathematician from a young age. After graduating in 1970 minimal surfaces and capillarity problems [4]. I had gradu- and fortuitously working on minimal surfaces—soap bubbles—he had ated from the University of Rome in 1970 and started my the idea of making a film. It was the start of a film series on art and career at the University of Ferrara, where I was very lucky mathematics, produced by his father and Italian state television. This to start working with Mario Miranda, the favorite student of article tells of the author’s professional life as a mathematician and a Ennio De Giorgi. At that time, I also met Enrico Giusti and filmmaker. Enrico Bombieri. It was the period of the investigations of partial differential equations, the calculus of variations and My father, Luciano Emmer, was a famous Italian filmmaker. the perimeter theory—which Renato Caccioppoli first intro- He made not only movies but also many documentaries on duced in the 1950s and De Giorgi and Miranda then devel- art, for example, a documentary about Picasso in 1954 [1] oped [5–7]—at the Italian school Scuola Normale Superiore and one about Leonardo da Vinci [2] that won a Silver Lion of Pisa. -
Fractals: a Resonance Between Art and Nature
Fractals: A Resonance between Art and Nature Richard Taylor, Ben Newell, Branka Spehar and Colin Clifford Physics and Psychology Reveal the Fractal Secrets of Jackson Pollock’s Drip Paintings The discovery of fractal patterns was an interesting advance in the understanding of nature [1, 2]. Since the 1970s many natural scenes have been shown to be com- posed of fractal patterns. Examples include coastlines, clouds, lightning, trees, rivers and mountains. Fractal patterns are referred to as a new geometry because they look nothing like the more traditional shapes such as triangles and squares known within mathematics as Euclidean geometry. Whereas these shapes are composed of smooth lines, fractals are built from patterns that recur at finer and finer magnifications, generating shapes of immense complexity. Even the most common of nature’s fractal objects, such as the tree shown in Figure 1, contrast 53 sharply with the simplicity of artificially constructed objects such as buildings. But do people find such complexity visually appealing? In particular, given peo- ple’s continuous visual exposure to nature’s fractals, do we possess a fundamental appreciation of these patterns – an affinity independent of conscious delibera- tion? The study of human aesthetic judgement of fractal patterns constitutes a rela- tively new research field within perception psychology. Only recently has research started to quantify people’s visual preferences for (or against) fractal content. A useful starting point in assessing people’s ability to recognize and create visual pat- ternsistoexaminethemethodsusedbyartists to generate aesthetically pleasing images on their canvases. More specifically, in terms of exploring an intrinsic ap- preciation of certain patterns, it seems appropriate to examine the Surrealists and their desire to paint images which are free of conscious consideration.