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  • H1-Hill-Snowflake-11

Robin Hill and Janko Gravner

SNOWFLAKES

Snowflake #4, 2011, cyanotype on paper, 96" X 96", collection of the artist

Snowflake #6, 2011, cyanotype on paper, 96" X 96", collection of the artist

Snowflake #7, 2011, cyanotype on paper, 96" X 96", collection of the artist

Snowflake #11, 2011, cyanotype on paper, 96" X 96", collection of the artist

*Robin Hill, Professor of Studio Art, and Janko Gravner, Professor of Mathematics, were awarded an Academic Senate  New Research Initiatives and Collaborative Interdisciplinary Research grant in 2011 for their research on data visualization and transformation of data sets to art forms.

In 2010, UC Davis Professors Robin Hill (Studio Art) and Janko Gravner (Mathematics) received a UC Davis Academic Senate’s New Initiative/Collaborative Research Awards Program grant for Digital Snowflake: From a Mathematical Model to an Art Model, to advance interdisciplinary research.   Their work explores current research on snow crystals. Such crystals, often called snowflakes, exhibit an intricate mix of geometric, chaotic, and stochastic form, vestiges of their growth from nanoscale water molecules to micron-scale branching to their final size of a few millimeters across. Ever since the pioneering observations of Kepler, Descartes, and Hooke four centuries ago, scientists have tried to learn how these crystals grow, but fundamental aspects of their dynamics, one of nature’s ultimate complex processes, remain a mystery. Although dependent on few physical parameters (primarily just three: temperature, pressure, and super- saturation of vapor), these crystals exhibit intricate morphology while retaining aesthetically pleasing symmetry and at least some measure of predictability. As controlled experiments with physical snowflakes are difficult and principles governing attachment of water vapor poorly understood, a mathematical model incorporating the attachment kinetics in terms of tunable parameters is a sensible scientific strategy. Classical macroscopic approach via dif- ferential equations is plagued by numerical instabilities, while realistic microscopic models with randomly diffusing particles are not computationally feasible due to the enormous number of degrees of freedom. Recently, the first mesoscopic three-dimensional model, able to replicate most observed snow crystal morphology, was devised by Gravner and his collaborator D. Griffeath. From small seeds, this parallel evolution self-organizes to form many features commonly observed in actual snowflakes: ridges, ribs, flumes and other “hieroglyphs,” side branches, emergent sandwich plates, hollow columns, hollow prism facets, and so forth.

The mesoscopic paradigm, building larger objects from convenient smaller scale modules, has its counterpart in Robin Hill’s art. Her work stems from the ideas of minimalism, or post-minimalism, the notion that meaning resides in process. Encompassing accidents and chance, Hill collects random materials, situations, phenomena, and then makes decisions to wrestle the collections into her artwork. Often the constituent objects are tiny and insignificant on their own, but through that act of claiming them and acknowledging them, and through their contribution to the whole, they become monumental. At the end, unlike a photographer, the artist makes her vision through her decisions and the mediation of touch.

Mathematically, the most important future direction of this research is into the role of randomness. Due to computational constraints, current models are deterministic, and digital images preserve the resulting perfect symmetry. Hill’s work introduces imperfections which make the artificial crystals both closer to the physical ones, and much more visually interesting. Comparing the mathematically induced randomness to visual effects of an interdisciplinary artist is in itself another interesting topic of study. In fact, chance is an important component of Hill’s work. Echoing Sufi philosophy, “Whatever you are looking for is looking for you too.” (Saul Williams), Hill’s art conveys the idea that “a lucky find reveals neither cosmic order nor chaos, but the mind of the finder — the chance event is a little bit of the world as it is, a world always larger and more complicated than an ordered and deterministic one would be. “ (Lewis Hyde on Chance and Creativity)

Gravner’s data visualizations utilize ray-tracing [POV], the graphics technique that translates an array of numbers into an ice crystal-like three dimensional object.   Rendering at the proper resolution (at least 100 megapixels) is costly and slow, even with optimization schemes. It is, however, remarkable how much ray- traced digital crystals have in common with cyanotypes, a 19th century photographic technique (historically used for botanical studies), utilized by Hill to create ghostly blue and white images by putting objects on light-sensitive paper. What the cyanotype records is the quality of translucence and opacity in a material, and also the distance the material is from the paper and any shadow it casts. There is a large measure of unpredictability in how the object, sitting on the paper, is going to read in cyanotype. Hill seeks those that have a sense of deep space within them, as if sitting behind the plane of the paper. The striking effects, compounded by the large scale of the artwork, cannot be conveyed by digital images alone. physical three-dimensional objects.

Robin Hill: The vantage point of my work is from inside form. I am interested in looking at and in describing the structures that underlie living things. The cyanotypes relate to fingerprints, DNA strands, or microscopic cultures in that they contain information that has the power to describe form. Light is the active ingredient and waiting is the passive ingredient in the cyanotypes. Placing objects and drawings on the sensitized paper reveals dimensions not visible to the naked eye. Matter is translated into degrees of opacity and translucency which are the two dimensional counterparts to thick and thin.

I am interested in exploring possibility and potential rather than articulating a finite resolution in my work. The subject of the work is work itself. Loosely construed accumulations of utilitarian materials or images figure as inventories or collections. Presumed hierarchies between disciplines are dissolved through their interchangeability and service to each other.

 

Janko Gravner:My specialty is the study of complex spatial processes, with particular focus on nucleation and growth phenomena. The models are inspired by, and intended to shed light on, processes far from equilibrium — they are partly based on modeling physical dynamics ranging from crystal growth, excitable media, and spread of infections, partly from ideas from computer science such as complexity and artificial life, and partly from a desire to understand the connections between local and global properties of an evolving system. On a deeper level, mathematics (and science) has always been partially motivated by search for elegance, symmetry, and a sort of ethereal beauty. It is therefore very exciting to start a conversation between the two worlds that are, for the most part, incomprehensibly disjointed: that of mathematics and that of art, to try to understand where they intersect and connect. The advances in graphical and printing capabilities of digital technology, which has a crucial and increasing impact on both mathematics and art, makes this a particularly appropriate time to do so.

In 2010, UC Davis Professors Robin Hill (Studio Art) and Janko Gravner (Mathematics) received a UC Davis Academic Senate’s New Initiative/Collaborative Research Awards Program grant for Digital Snowflake: From a Mathematical Model to an Art Model, to advance interdisciplinary research.   Their work explores current research on snow crystals. Such crystals, often called snowflakes, exhibit an intricate mix of geometric, chaotic, and stochastic form, vestiges of their growth from nanoscale water molecules to micron-scale branching to their final size of a few millimeters across. Ever since the pioneering observations of Kepler, Descartes, and Hooke four centuries ago, scientists have tried to learn how these crystals grow, but fundamental aspects of their dynamics, one of nature’s ultimate complex processes, remain a mystery. Although dependent on few physical parameters (primarily just three: temperature, pressure, and super- saturation of vapor), these crystals exhibit intricate morphology while retaining aesthetically pleasing symmetry and at least some measure of predictability. As controlled experiments with physical snowflakes are difficult and principles governing attachment of water vapor poorly understood, a mathematical model incorporating the attachment kinetics in terms of tunable parameters is a sensible scientific strategy. Classical macroscopic approach via dif- ferential equations is plagued by numerical instabilities, while realistic microscopic models with randomly diffusing particles are not computationally feasible due to the enormous number of degrees of freedom. Recently, the first mesoscopic three-dimensional model, able to replicate most observed snow crystal morphology, was devised by Gravner and his collaborator D. Griffeath. From small seeds, this parallel evolution self-organizes to form many features commonly observed in actual snowflakes: ridges, ribs, flumes and other “hieroglyphs,” side branches, emergent sandwich plates, hollow columns, hollow prism facets, and so forth.

The mesoscopic paradigm, building larger objects from convenient smaller scale modules, has its counterpart in Robin Hill’s art. Her work stems from the ideas of minimalism, or post-minimalism, the notion that meaning resides in process. Encompassing accidents and chance, Hill collects random materials, situations, phenomena, and then makes decisions to wrestle the collections into her artwork. Often the constituent objects are tiny and insignificant on their own, but through that act of claiming them and acknowledging them, and through their contribution to the whole, they become monumental. At the end, unlike a photographer, the artist makes her vision through her decisions and the mediation of touch.

Mathematically, the most important future direction of this research is into the role of randomness. Due to computational constraints, current models are deterministic, and digital images preserve the resulting perfect symmetry. Hill’s work introduces imperfections which make the artificial crystals both closer to the physical ones, and much more visually interesting. Comparing the mathematically induced randomness to visual effects of an interdisciplinary artist is in itself another interesting topic of study. In fact, chance is an important component of Hill’s work. Echoing Sufi philosophy, “Whatever you are looking for is looking for you too.” (Saul Williams), Hill’s art conveys the idea that “a lucky find reveals neither cosmic order nor chaos, but the mind of the finder — the chance event is a little bit of the world as it is, a world always larger and more complicated than an ordered and deterministic one would be. “ (Lewis Hyde on Chance and Creativity)

Gravner’s data visualizations utilize ray-tracing [POV], the graphics technique that translates an array of numbers into an ice crystal-like three dimensional object.   Rendering at the proper resolution (at least 100 megapixels) is costly and slow, even with optimization schemes. It is, however, remarkable how much ray- traced digital crystals have in common with cyanotypes, a 19th century photographic technique (historically used for botanical studies), utilized by Hill to create ghostly blue and white images by putting objects on light-sensitive paper. What the cyanotype records is the quality of translucence and opacity in a material, and also the distance the material is from the paper and any shadow it casts. There is a large measure of unpredictability in how the object, sitting on the paper, is going to read in cyanotype. Hill seeks those that have a sense of deep space within them, as if sitting behind the plane of the paper. The striking effects, compounded by the large scale of the artwork, cannot be conveyed by digital images alone. physical three-dimensional objects.

Robin Hill: The vantage point of my work is from inside form. I am interested in looking at and in describing the structures that underlie living things. The cyanotypes relate to fingerprints, DNA strands, or microscopic cultures in that they contain information that has the power to describe form. Light is the active ingredient and waiting is the passive ingredient in the cyanotypes. Placing objects and drawings on the sensitized paper reveals dimensions not visible to the naked eye. Matter is translated into degrees of opacity and translucency which are the two dimensional counterparts to thick and thin.

I am interested in exploring possibility and potential rather than articulating a finite resolution in my work. The subject of the work is work itself. Loosely construed accumulations of utilitarian materials or images figure as inventories or collections. Presumed hierarchies between disciplines are dissolved through their interchangeability and service to each other.

 

Janko Gravner: My specialty is the study of complex spatial processes, with particular focus on nucleation and growth phenomena. The models are inspired by, and intended to shed light on, processes far from equilibrium — they are partly based on modeling physical dynamics ranging from crystal growth, excitable media, and spread of infections, partly from ideas from computer science such as complexity and artificial life, and partly from a desire to understand the connections between local and global properties of an evolving system. On a deeper level, mathematics (and science) has always been partially motivated by search for elegance, symmetry, and a sort of ethereal beauty. It is therefore very exciting to start a conversation between the two worlds that are, for the most part, incomprehensibly disjointed: that of mathematics and that of art, to try to understand where they intersect and connect. The advances in graphical and printing capabilities of digital technology, which has a crucial and increasing impact on both mathematics and art, makes this a particularly appropriate time to do so.

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