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Timetable (GFSW04)

Form in art, toys and games

Tuesday 28th November 2017 to Friday 1st December 2017

Tuesday 28th November 2017
09:00 to 09:20 Registration
09:20 to 09:30 Welcome from David Abrahams (INI Director)
09:30 to 10:10 Michael Berry
Magic mirrors and magic windows
Ancient oriental mirrors possess a property that seemed magical and was probably unintended by those who made them: the pattern embossed on the back of such a mirror appears in light reflected onto a screen from its apparently featureless front surface. In reality, the embossed pattern is reproduced on the front, in low relief invisible to direct observation, and analysis shows that the projected image results from pre-focal ray deviation. In this interesting regime of geometrical optics, the image intensity is given simply by the Laplacian of the height function of the relief. Observation confirms this ‘Laplacian image’ interpretation, and indicates that steps on the reflecting surface are about 400 nm high, explaining their invisibility. Current research aims to create the transparent analogue of the magic mirror: ‘magic windows’, in which glass sheets, flat to unaided vision but with gentle surface relief, concentrate light onto a screen with intens ity reproducing any desired image. Laplacian image theory implies that the desired surface relief is obtained by solving Poisson’s equation.

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10:10 to 10:50 Denis Weaire
Artful foams: in memoriam Cyril Stanley Smith
Cyril Stanley Smith was a distinguished metallurgist who eventually left that discipline to pursue a wider interest in science and technology, and their relation to art. He was critical of his contemporaries, as being too preoccupied with thepursuit of perfect idealised order. Although his ideas were tentative he was(like D’Arcy Wentworth Thompson) a prophet. As such he inspired others,including the present speaker, who will describe his adventures with foam (afavourite prototype of Smith), taking him into art and architecture as Smith would have liked - for scientists, he said, should be playful.
10:50 to 11:10 Morning Coffee
11:10 to 11:50 Aubrey Jaffer
Physics and mathematics of marbling
Co-authors: Shufang Lu (Zhejiang University of Technology), Xiaogang Jin (Zhejiang University), Fei Gao (Zhejiang University of Technology), Xiaoyang Mao (University of Yamanashi)

Ink marbling refers to techniques for creating intricate designs in colored inks floating on a liquid surface. If the marbling motions are executed slowly, then this layer of inks can be modeled as a two-dimensional incompressible Newtonian fluid. In this highly constrained model many common marbling techniques can be exactly represented by closed-form homeomorphisms. These homeomorphisms can be composed and compute the composite mapping at any resolution orders of magnitude faster than finite-element fluid-dynamics methods.Pictorial designs for flowers and animals use short strokes of a single stylus; presented is a closed form velocity field for Oseen fluid flow and its application to creating short stroke marbling homeomorphisms.These approaches extend to three-dimensions and allow creation of coherent marbled surfaces on any shape while avoiding the process of texture mapping entirely.

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11:50 to 12:30 Allan McRobie
Catastrophe theory and art
As described in my book The Seduction of Curves, published by Princeton University Press in August 2017, there are strong links between Catastrophe Theory and many spheres of art. This talk will explore those historical links - most notably via the works of Salvador Dali and the Constructivist artist Naum Gabo. Extending beyond the book, the talk will also look at what possible new avenues this may open up for creative exploration in art and architecture, ranging from light-based works through to a proposed large scale structure/sculpture for the forthcoming Chelsea Flower Show.
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:10 Roberto Zenit
Hydrodynamic instabilties and modern artistic painting
Co-author: Sandra Zetina (Universidad Nacional Autonoma de Mexico)

Painting is a fluid mechanical process. The action of covering a solid surface with a layer of a viscous fluid is one of the most common human activities; virtually all manmade surfaces are covered with a layer of fluid, which eventually cures and solidifies, to provide protection against the environment or simply for decoration. The process of applying layer of fluid of uniform thickness on a surface has been vastly studied and it is well understood. In the case of artistic painting, the objective is different. Painters learn how to manipulate the fluid, through lengthy empirical testing of the action and the physical properties of the fluids, to create textures that can be used to create patterns and compositions of aesthetic value. In other words, artists aim to create non uniform paint coatings, produced at will and in a controlled manner. It has been recently identified that, for the case of modern artistic painting, one successful way to create such patterns is by provo king hydrodynamic instabilities in a controlled manner. In this presentation we analyze several particular cases used by notable modern artists in their works: David A. Siqueiros used the Rayleigh-Taylor instability for his ‘accidental painting’ technique; Jackson Pollock learned to control the curling instability of viscous filaments in his dripping technique; Max Ernst used the Saffman-Taylor instability to paint with decalcomanias, etc. Furthermore, we analyze other modern painting techniques and their relation with modern and very active fluid mechanics areas of research. We also discuss the importance of the properties of modern materials and how their evolution could have influenced the emergence of new artistic painting techniques. The aim of this investigation is to create an explicit relation between the body of knowledge of modern fluid mechanics and those of art history and conservation.

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14:10 to 14:50 Andrzej Herczynski
Paul Klee notebooks: form and mathematics
Paul Klee was one of the most prolific and original painters of the first half of the 20th century. Although he was influenced by Picasso, Kandinsky, and other contemporary artists, and engaged with Der Blaue Ritter, he forged his own artistic path apart from the currents such as cubism or surrealism. He was a dedicated art teacher, and left extensive notes for his lectures at the Bauhaus (1921-31). The notes were published in two volumes The Thinking Eye and The Nature of Nature, and constitute, in effect, Klee’s treatise on geometrical aspects of forms, perspective, motion and its depiction, growth, and many other topics. This presentation is a selective consideration of Klee’s recurring themes and a naïve attempt to organise them according to their mathematical and physical concepts.
14:50 to 15:15 Jane Wang
Music of falling paper
A piece of paper falls in a seemingly erratic manner. Each fall is a solution to the Navier-Stokes equations, but why does it evoke such a poetic feelings in us? When our eyes trace the paper as it falls, following its flutter and tumble, punctuated by a sudden lift and turn, we can feel lines of musical phrases in air. Some motions have the sound of percussion, others of a flute, a string, or even a cry or laugh. Drop small ones en mass, and they become fireworks.

I started making ‘Music of Falling Paper’ a few years ago. It is an attempt to use falling paper both as a ‘music instrument’ and a visual means to convey the connection between the movement of simple objects and the movement of living organisms. They are improvisational pieces, often in collaboration with musicians, in public space and in response to the theme of the event. I drop pieces of paper from a height, the musicians improvise, and I in turn respond to their play when choosing the next sequence to drop. When constructing the sequences, I think about many things. I shall share some of these thoughts and clips at the talk.

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15:15 to 15:30 Jane Wang
Music of falling paper – performance in the foyer
15:30 to 16:00 Afternoon Tea
16:00 to 16:40 Alex Bateman
Paper mosaics: an exploration of tiling’s through origami
Origami tessellations are a form of paper folding that first arose in the 1960s that repeats a simple origami unit to tile the plane. In this presentation I will explain how over the last 20 years folders have explored the space of mathematical tilings, as well as describe some of the tools and techniques that are used to transform tilings into foldable origami structures.

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16:40 to 17:20 Tomohiro Tachi
Computational Origami Design
Folding is a universal principle that appears both in nature and artifacts. Folding can enable various shapes from thin sheets through self-constrained complex kinematic motion. The speaker talks about computational origami, i.e., the geometry and the algorithm of origami, and its application to design. The topics involve origamizer, a universal algorithm to fold any polyhedral shape from a sheet of paper; rigid origami, the kinematics of plate and hinges utilizing its flat and singular state; computational (and actual) hardness of folding compared to unfolding; and metamaterials exploiting the geometry of origami.
17:20 to 18:20 Welcome Wine Reception at INI
Wednesday 29th November 2017
09:00 to 09:40 Jean-Marc Chomaz
Art & Science, the big trail
Is science a territory and can the current Art & Science movement transform it by transplanting artists into "residence"? Do we enter into the era of the conquest of science, good scientists in the new myth of the frontier; should the artist pace the unknown of his gesture, descending the cliffs of The Big Trail to the conquest of a valley of knowledge? The knowledge is folded and complex; the implantation of artist on the territory of science, authorizes postures of ethnologist, colon or explorer but to penetrate this world of spirits we must accept the indigenous miscegenation. My practice Arts & Sciences is deeply rooted in this crossbreeding, this hybridization. A shared journey between artists and scientists, leads to a sensitive exploration of the logical spaces of regular appearance, of future non-existents. The group can also be renamed to the slope and deny the gravity by not following only the deductive lines. One route will become art and the other will become science, but in these shared journeys, each will become the other, revealing the sensitive side of science, meeting the Giants of Light. For me a common work Art & Science leads to this double initiation transforming the very nature of the sciences, questioning the value of the model, the truth and the proof.

This posture of artist-scientist rehabilitates science as an act of the mind, imaginary made of interrogations and projections of the sensible real. The logical universes are jealous of their mysteries, dark matter, foliated and sooty energy, they are infinite measured by the mesure of the proof. They often pour into submerged areas. To survey them as an artist, without believing in the rolling of stones, opens other valleys perched in the folds of the rock. Three holes drawn on the surface of a box and the space of nine trays conceals a hidden sheep of the ephemeral Prince.

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09:40 to 10:20 Mimi Koehl
Art in aid of science
I was an art major as an undergraduate before being lured into biomechanics and biofluiddynamics by the beauty of natural forms, both living and physical.  Since I have done both art and science, I see two striking similarities between the two pursuits.   One is careful observation of the natural world  (but scientists have tools that let us "see" more than artists can see with their eyes alone).  The other is the use of abstraction to capture the essence of something (objects, processes), although the "language" used to communicate the abstraction is visual for the artist, while it is also mathematical for the scientist.  Most of this workshop focuses on how science and mathematics can inform and inspire art, but I will provide some examples from my own work of how collaboration with artists can aid scientific research.
10:20 to 11:00 Stephen Morris
Art, outreach, and pattern formation
For the past several years, I have been experimenting with the boundary between art and science. I have repurposed my scientific images of pattern formation experiments and pattern-forming natural phenomena by presenting them as art. I have exhibiting images and videos in art galleries and juried art shows. I have brought artists into my research lab for several hands-on workshops. I am the co-organizer of the "ArtSci Salon", an evening meet-up group at the Fields Institute of Mathematical Science in Toronto. I have released a trove of icicle shape data for free use under the Creative Commons. I have collaborated with sound artists and composers to use pattern formation images and videos as input to their creative processes. All these activities can be viewed equally as art-making or as scientific outreach. The scientific field of pattern formation has developed a distinct aesthetic sensibility, informed by mathematics and physics, but inherently visual and dynamic. This aesthetic is an essential motivation for this work. This talk will describe my experiences in this "application" of pattern formation to making, exhibiting and discussing art. My experience shows that unmodified scientific images can be well received as art and generate wide-ranging conversations across traditionally separate disciplines. The art world offers an interesting venue for science outreach activities, as well as being a lot of fun to explore. The ArtSci Salon:
The Icicle Atlas:
Flickr stream:
11:00 to 11:30 Morning Coffee
11:30 to 12:10 Carola-Bibiane Schönlieb (University of Cambridge); (Cambridge Mathematics of Information in Healthcare)
Mathematical approaches for virtual art restoration
Virtual image restoration, also called image inpainting, denotes the process whereby missing or occluded parts in images are filled in based on the information provided by the intact parts of the image. In this talk I will sketch and motivate different mathematical principles that can guide a digital restoration attempt. Digital photographs of art pieces are essentially mathematical objects, and this puts the vast toolbox of mathematics at the restorers’ fingertips. We will encounter the role of differential equations and patch-based methods for virtually restoring structure, texture and colour in images. In particular, we will show examples from the restoration of the Neidhart frescoes (Tuchlauben, Vienna), the restoration of a painting by Sebastiano Del Piombo (the Hamilton Kerr Institute, The Fitzwilliam Museum), and the unearthing of hidden structures in illuminated manuscripts revealed by infrared imaging (the MINIARE project, the Fitzwilliam Museum). After a critical discussion of restoration results I will conclude by pointing out the capabilities and limitations of digital restoration methods, and provide some hints towards applications of such mathematical approaches that go beyond the restoration of arts – such as medicine, forensics and geography.
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 13:45 Mella Shaw
Artists’ Session: In pursuit of tipping point
13:45 to 14:00 Mark Francis
Artists' Session: Mark Francis
14:00 to 14:15 Emma Rodgers
Artists' Session: Emma Rodgers
14:15 to 14:30 Henry Jabbour
Artists' Session: The Human Form - In Search of the Universal
14:30 to 14:45 Nedyalka Panova
Artists' Session: On the Border of Consciousness
14:45 to 15:00 Manoel Veiga
Artists' Session: How science inspired my work
15:00 to 15:15 Ulyana Gumeniuk-Parker
Artists' Session: Perception of form. Lessons form art history
15:15 to 15:30 Melissa Murray
Artists' Session: Material and Metaphor
15:30 to 15:45 Paul Friedlander
Artists' Session: Serendipity & the wave
15:45 to 17:00 Exhibition opening and viewing (wine reception)
Thursday 30th November 2017
09:30 to 10:10 Keith Moffatt
The beaver ball: a chaotic rolling robot
Equations describing the rolling of a spherical ball on a horizontal surface are obtained, the motion being activated by an internal rotor driven by a battery mechanism. The rotor is modelled as a point mass mounted inside a spherical shell, and caused to move in a prescribed circular orbit relative to the shell. The system is described in terms of four independent dimensionless parameters. The equations governing the angular momentum of the ball relative to the point of contact with the plane constitute a six-dimensional, non-holonomic, non-autonomous dynamical system with cubic nonlinearity. This system is decoupled from a subsidiary system that describes the trajectories of the center of the ball. Numerical integration of these equations for prescribed values of the parameters and initial conditions reveals a tendency towards chaotic behaviour as the radius of the circular orbit of the point mass increases (other parameters being held constant). It is further shown that there is a range of values of the initial angular velocity of the shell for which chaotic trajectories are realised while contact between the shell and the plane is maintained. The predicted behaviour has been observed in our experiments.  

Work in collaboration with V.A.Vladimirov and K. Ilin
10:10 to 10:50 Daniel Goldman
“Fun”-damental physics: robophysical models for General Relativity and Quantum Mechanics
What happens when physicists build robots? In my group, we do not view these machines as labor-saving devices or demonstrations of control principles, but as scientific instruments, with which to have fun and study fascinating new dynamical systems. We call this approach “robophysics” (see Aguilar et al, Rep. Prog. Phys., 2016), and in this talk I will highlight two of our recent studies in which we observe aspects of “fundamental” (or “modern”) physics in simple self-propelling robots. 1) When transiting a regular array of rigid posts, a ~80 cm long slithering snake-like robot passively scatters into preferred directions, the extent of which is inversely related to the post spacing; these behaviors thus mimic aspects of matter waves complete with diffraction patterns, the diffraction-pattern destroying “measurement” phenomena, Poisson spots, an uncertainty principle, and the beautiful Talbot carpet (a near-field diffraction effect). Of course, there is nothing quantum mechanical about our system: a model based upon robot head-post collisional dynamics and interference of neighboring posts captures much of the observed dynamics. 2) Inspired by the standard (but inaccurate) science-museum type demonstration of General Relativity (e.g. marbles orbiting a central depression), we create an experiment in which the orbiting mass does not lose energy and thus displays persistent dynamics. When confined to a ~2 m diameter flexible spandex sheet with an imposed central depression, a ~10 cm diameter circular two-wheeled robot car executes trajectories that have aspects of orbits in the Schwarzschild solution to Einstein’s field equations in General Relativity (GR). Our system displays closed orbits (like in Newtonian gravity) as well as beautiful patterns of precessing orbits. The latter obey a precession formula derived from the Schwarzschild solution, but with negative precession, indicating that the GR-like correction term in our system acts to repel orbits. In addition to the fun one can have with these systems, we argue that robophysical devices have educational utility: students (and faculty) of all ages gain insight into a diversity of natural phenomena via hands-on construction and play using low-cost but sophisticated  devices.
10:50 to 11:10 Morning Coffee
11:10 to 11:50 Alain Goriely
Playing with magnetic chains: from self-buckling to self-assembly
Spherical neodymium-iron-boron magnets are marketed as toys as they can be assembled into different shapes due to their high magnetic strength. In particular, we consider two simple structures, chains and cylinders of magnets. By manipulating these structures, it quickly appears that they exhibit an elastic response to small deformations. Indeed, chains buckle on their own weight, rings oscillate, and cylinders resist bending but recover their shape after poking. A natural question is then to understand the response of these structures based on the individual physical properties of the magnets and to understand to what extent they behave elastically. In this talk, I will show through illustrative experiments and simple model calculations that the idea of an effective magnetic bending stiffness is, in fact, an excellent macroscopic characterisation for the mechanical response of magnetic chains. I will then propose a more rigorous approach of the problem by considering discrete-to-continuum asymptotic analysis to derive a continuum model for the energy of a deformed chain of magnets based on the magnetostatic interactions between individual spheres.
11:50 to 12:30 Pierre Degond
Collective dynamics of bristlebots
Bristlebots are very simple small robots that are commercialized under different names as toys for children (and adults). They seem to have inspired many youtubers. In a joint work with E. Climent, F. Plouraboue and O. Praud from Toulouse fluid mechanics lab IMFT, G. Dimarco from Ferrara and my former student T. B. N Mac, we have studied the dynamics of swarms of bristlebots confined in a disk and an annulus. The talk will report on the experimental and modelling results and will feature some live experiments. 
12:30 to 13:30 Lunch @ Wolfson Court
13:30 to 14:10 Yuli D Chashechkin
Self-propelled wedge
2D flows around neutral buoyancy wedge submerged in a tank with continuously stratified fluid were calculated using conventional time-dependent governing equations set in frame of OpenFOAM codes. Fine structure of different variables fields (density or pressure and their gradients, velocity, vorticity, rate of energy dissipation) was analyzed in wide range of the problem geometry and stratification. Numerical results are compared with data of schlieren visualization of the self-moving wedge in the laboratory tank.
14:10 to 14:50 Patrick Weidman
On the terminal motion of sliding/spinning discs
We review the classic problem concerning the terminal motion of a slidingspinning disk on a horizontal surface which shows that sliding and spinningstop at the same time with terminal value ǫ0 = 0.653, where ǫ = v(t)/Rω(t)is the ratio of linear speed to tip speed of a disk of radius R.We then generalize to problem to find the terminal motion of annular disksand two-tier disks. For the annular disk the terminal speed ratio ǫ0 rangesfrom 0.653 to 1 as the radius ratio η = Rin/Rout varies from 0 to 1. Fortwo-tier disks composed of a lower disk of radius R1 and height H1 attachedto upper disk of radius R2 and height H2, one has a two parameter problemdefined by η = R1/R2 and λ = H1/H2. In addition to simultaneous terminalstopping motions, we find, for small regions in η − λ parameter space, thatthe two-tier disk can either stop spinning first and slide to rest, or stop slidingand spin to rest. An experiment is devised to capture these unique terminalmotions.
14:50 to 15:30 L Mahadevan
Geometry and probability in perception and action
How do you design a coin that lands on its edge 1/3 of the time ? How might one throw accurately ? How does one walk along a straight line ? How can one visualize chance ? Each of these problems invokes geometric concepts in a probabilistic setting. I will discuss solutions to some of these problems that lie at the intersection of cognition, neuroscience and behavior -  and thus are of relevance to art and science.
15:30 to 16:00 Afternoon Tea
16:00 to 16:30 Neil Ribe
An Introduction to the Mechanics of the Lasso
Co-authors: Pierre-Thomas Brun (Dept. of Chemical Engineering, Princeton University, Princeton, NJ USA), Basile Audoly (Laboratoire LMS, Ecole Polytechnique, Palaiseau, France)

Trick roping evolved from humble origins as a cattle-catching tool into a sport that delights audiences with its complex patterns or ‘tricks’. Its fundamental tool is the lasso, formed by passing one end of a rope through a small loop (the honda) at the other end. Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane. We first consider the case of a fixed (non-sliding) honda. Noting that the rope’s shape is steady in the reference frame rotating with the hand, we analyse a string model in which line tension is balanced by the centrifugal force and the rope’s weight. We use numerical continuation to classify the steadily rotating solutions in a bifurcation diagram and analyse their stability. In addition to Flat Loops, we find planar ‘coat-hanger’ solutions, and whirling modes in which the loop collapses onto itself. Ne xt, we treat the more general case of a honda that can slide due to a finite coefficient of friction of the rope on itself. Using matched asymptotic expansions, we resolve the shape of the rope in the boundary layer near the honda where the rope’s bending stiffness cannot be neglected. We use this solution to derive a macroscopic criterion for the sliding of the honda in terms of the microscopic Coulomb static friction criterion. Our predictions agree well with rapid- camera observations of a professional trick roper and with laboratory experiments using a ‘robo-cowboy’.
16:30 to 17:10 Raymond Penner
Physics of Sports
Sporting activities provide great examples of physics in action. Participants and observers are often intrigued by the design or motion of a particular piece of sporting equipment. Physicists are intrigued by these same questions. Topics that will be considered in the presentation will include the behavior of a curling rock, the design of a clubhead in the game of golf, and a look at the physics behind the variety of pitches thrown in the game of baseball.
17:10 to 17:50 Christophe Clanet
Forms in Olympic Games
Rowing has been part of the summer Olympics since its debut in 1896. The shape of the boat has slightly changed. We will discuss the origin of this shape with a special attention to the aspect ratio, which can reach values as high as 30, much larger than any other boat. In a second part, we will move to ball games and will focus on zig-zag trajectories which are (sometimes) observed in volley, soccer and golf.
19:30 to 22:00 Formal Dinner at Murray Edwards College
Friday 1st December 2017
09:30 to 17:00 Outreach Day: Form & Deformation in Art, Toys, and Games INI 1
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons