# User Portlet

Featured Contributor

Clayton Shonkwiler

Colorado State University

LOCATION: Fort Collins, CO

WEBSITE: http://shonkwiler.org

INTERESTS IN JOBS & NETWORKING:

ABOUT ME:

I am a mathematician and artist.

I am interested in geometric models of physical systems; currently I'm mostly focused on geometric approaches to studying random walks with topological constraints, which are used to model polymers.

My art is often inspired by the mathematics that arise in my research and teaching, but more generally I enjoy turning interesting and non-trivial mathematics into art.

Prints available at https://shonkwiler.org/store

STAFF PICKS:

- [GIF] Separation Anxiety (Level sets of the torus)
- Fade in, fade out: isometric projection of squares
- [GIF] Epicenter (Spinning hexagons)
- [GIF] Play (Conformal transformation of the square grid)
- [GIF] Reinvention (Morphing the triangular grid)
- [GIF] Transition (Shifting string art)
- [GiF] Come Along (Square wave interpolants)
- [GIF] Interstellar (A Closed Geodesic in 17-Gon Space)
- [GIF] Small multiples (spinning rhombuses)
- [GiF] ℘' (Conformal transformation of hexagonal grid)
- [GiF] Modular Flow
- [GiF] Stay Upright (Projective view of Hopf circles)
- [GIF] Strange Duality
- [GIF] Dodecapod (Images of radial lines under Schwarz-Christoffel mapping)
- [GIF] Trilateral (String art)
- [GiF] Shifting Lands (Level sets of x*y*z)
- [GiF] Descent (Shrinking octagons)
- [GiF] Light Show (Rotating hyperboloid)
- [GiF] Dig In (Stereographic image of concentric circles)
- [GiF] Cyclic Family (Dancing lines representing cyclic quadrilaterals)
- [GIF] Hex (Rotating Hexagons)
- [GIF] Interference (Stereographic projections of lesser circles)
- [GIF] Rise Up ((29, 5)-torus knot)
- [GIF] Random Lines (8 frames of 20,000 random lines each)
- [GiF] Envelope (String art)
- [GIF] Under Scrutiny (Level sets of the 3-norm on the unit sphere)
- Stiefel Manifolds and Polygons
- [GiF] Tangents (Tangent lines to a Bessel function)
- Probability Theory of Random Polygons from the Quaternionic Viewpoint
- [GiF] Tetra (Stereographic projections of concentric annuli)
- [GiF] Lean In (rotating sphere)
- [GIF] Recut (Cone Net Animation)
- [GiF] Facile à Retenir (Permutohedron-inspired animation)
- [GIF] RGB (Spinning triangles)
- [GIF] Just Squares (Pattern from spinning squares)
- [GIF] Correlations (Mercator projection of contours for dot product sum)
- [GIF] Come Around (Spheres traversing a torus knot)
- [GIF] Limits (Möbius transformations of the triangular tiling)
- [GIF] Loop (Geodesics in quadrilateral space)
- [GIF] Gerontocracy (circular slices of a triangle)
- [GIF] Around the Bend (Rotating regular polygons)
- [GIF] Ruled (doubly ruled surface)
- [GIF] Ennea (nonagons centered on unit circle)
- [GIF] Sweep Out
- [GIF] Scherk surface and family resemblance
- [GIF] Obfuscate (Repeated pattern)
- [GIF] Snap to Grid (Deforming the square grid)
- [GIF] Dawn (Image of square grid under cosine)
- [GIF] To Infinity ((2,1) torus knot)
- [GIF] Riemann Hypothesis video from Quanta Magazine
- [GIF] Between (Stereographic projection of circles of latitude)
- [GIF] Wrap: wrapping lines around a circle
- [GIF] △▽ (Morphing triangle grid)
- [GIF] Cross Sections (Slices of the cuboctahedron)
- [GIF] ■□ (Rotating blocks)
- [GIF] Omnitruncated (More permutohedra)
- [GIF] Rise (Conformal image of parallel lines)
- [GIF] Vanishing Point (Conformal image of a vertical grid)
- [GIF] Nines (Minimum-stick 9-crossing knots)
- [GIF] Square Grid (Schwarz–Christoffel mapping from circle to square)
- [GIF] Rotation Redux (Inverse Cayley transform of rotating grid of circles)
- [GIF] Fourth Power (Fourth power of a square grid in the complex plane)
- [GIF] :christmas_tree: (Conformal map of upper half-plane to triangle)
- [GIF] :globe_with_meridians: (Inverse Cayley transform of contours of log)
- [GIF] :globe_with_meridians: (Inverse Cayley transform of contours of log)
- [GIF] :eyes: (Infinite Steiner chain)
- [GIF] Cube Life (Stereographic projection of rotating cube vertices)
- [GIF] Framing (Morph between +3-framed and 0-framed 200-gons)
- [GIF] Schools Out (Stereographic projection of random sphere paths)
- [GIF] Pathways (Some random paths on the sphere)
- [GIF] Five Easy Pieces (Rotating truncation of the tetrahedron)
- [GIF] Master Control Program (Minimal 7_4 knot on the simple cubic lattice)
- [GIF] Home on the Range (Rotating minimal 7_7 on the BCC lattice)
- [GIF] BCC (Minimal figure-eight knot on the body-centered cubic lattice)
- [GIF] Symmetric Minimality (symmetric lattice trefoil knot)
- [GIF] Minimal (Rotating minimal lattice trefoil knot)
- [GIF] Recede (Concentric circles gradient)
- [GIF] Dropped Call (Histogram of Dirichlet-distributed barycentric coords)
- [GIF] Fitting In (Stereographic projection of 124-circle packing on sphere)
- [GIF] Dance (Chladni figures for a square drum)
- [GIF] Bounce ((3,1)+(1,3) vibration mode of a square membrane)
- [GIF] Rolling (Circles rolling inside a circle)
- [GIF] Double Projection (Projected rotating 16-cell)
- [GIF] J34 (Hopf projection of the 600-cell)
- [GIF] This is Only a Test (Decagons from stereographic projections)
- [GIF] Omnes Pro Uno (Mercator projection of level sets of dot product sum)
- [GIF] Power Surge (Mercator projection of level sets)
- [GIF] Map (Mercator projection of great circles)
- [GIF] In Balance (Mercator projection of concentric circles on the sphere)
- [GIF] Unfold (Octagon to 16-gon transition)
- [GIF] Follow Through (Morphing 11-pointed star)
- [GIF] Fall In (Stereographic projection of dots on the sphere)
- [GIF] Twist (Spinning lines)
- [GIF] Loxo (Voronoi cells of stereographically projected loxodrome points)
- [GIF] Caught (Voronoi cells of stereographically projected pattern)
- [GIF] Small Changes (Hamiltonian cycle on the great rhombicosidodecahedron)
- Platonic (Stereographic projections of the Platonic solids)
- [GIF] All Day (Hamiltonian cycle on the 24-cell)
- [GIF] How Does That Work? (Hamiltonian cycle on the 5-cell)
- [GIF] Throw (Hamiltonian cycle on the 120-cell)
- [GIF] Fall Out (Rotating circle on the projective plane)
- [GIF] Microcosm (Stereographic projection of cube grid)
- [GIF] Inside (Stereographic projection of points on the Clifford torus)
- [GIF] Touch ’Em All (Hamiltonian cycle on the hypercube)
- [GIF] Send/Receive (Stereographic projection of latitude/longitude grid)
- [GIF] Who's the Boss? (Stereographic projection of a pyramid)
- [GIF] Flat (Stereographic projection of flat torus)
- [GIF] Vitals (Animated von Mises distribution)
- [GIF] Trifolium (Envelope of the trifolium curve)
- [GIF] Grid (Transformation of the square grid)
- [GIF] Thread the Needle (Envelope of an ellipse)
- [GIF] Bertrand Pairs (Bertrand pairs of a helix)
- [GIF] Osculating (Osculating circles to a polar curve)
- [GIF] Eyes Wide (Stereographic projection of spherical circle packing)
- [GIF] Pack It In (Stereographic projection of circles)
- [GIF] Part of the Journey (Conformally transformed hex circle packing)
- [GIF] Self-Dual (Rotating 24-cell)
- [GIF] Circle Back (Stereographic recursive circle packing)
- [GIF] Grassfire (Parallels of the limaçon trisectrix)
- [GIF] Stereo Vision (Stereographic projection of a (24, 23)-torus knot)
- [GIF] Back and Forth (Möbius transformations of the circle)
- [GIF] Inevitability ((7, 3)-torus knot)
- [GIF] Orthoplex (Stereographic projection of a rotating 16-cell)
- [GIF] Going Nowhere (Sphere with loxodromic trajectories)
- [GIF] Horizon (Marching lines)
- [GIF] Renewable Resource (More Möbius transformations of the sphere)
- [GIF] Interlock (Rotating Clifford torus/Hopf fibration)
- [GIF] Inner Light (Möbius transformations of the sphere)
- [GIF] Fire in the Hole (Spheres on logarithmic spirals)
- [GIF] Toss (Projectile envelope)
- [GIF] Bessel (Taylor approximations to a Bessel function)
- [GIF] Canis (Circle transformation)
- [GIF] Turn, Magic Wheel (Spinning squares)
- [GIF] Come Together (Spinning hexagons)
- [GIF] Go Deeper (Whirl infinite zoom)
- [GIF] Advance (Morphing squares)
- [GIF] Step Out (Recursive triangle morph)
- [GIF] Isotomic (Isotomic conjugates of edge parallels)
- [GIF] Isogonal (Isogonal conjugates of edge parallels)
- [GIF] Re-Tie (Torus knot morph)
- [GIF] Things That Go Bump in the Night (Vibrational mode of the triangle)
- [GIF] Source (Expanding diamonds)
- [GIF] Around and Around (Stereographic projection of rotating circles)
- [GIF] Hamiltonian (Circuit of octahedra)
- [GIF] Up and Down (Broken triangular grid)
- [GIF] Move Along (Envelopes of conic sections)
- [GIF] Back Away (Alternated cubic honeycomb)
- [GIF] Stripes (Hyperbolic geodesics)
- [GIF] Give Me Some Space (Rectification of the Tetrahedron)
- [GIF] Cloud (Configuration space of pentagons)
- [GIF] Center of Mass (Conformal transformations)
- [GIF] A to Z (Image morph)
- [GIF] Exchange (Interchanging cubes)
- [GIF] Hidden Depths (Reflections in a Disk)
- [GIF] Catecoid (Catenoid/Helicoid associate family)
- [GIF] Magic Carpet (Plane waves)
- [GIF] Good Vibrations (Chladni patterns on the disk)
- [GIF] Shock (Spinning squares)
- [GIF] The Band Plays On (Chladni figures for a square drum)
- [GIF] Square Up (Trig surface animation)
- [GIF] Compression (Deforming the hex lattice)
- [GIF] Drumbeat (Vibration mode of a circular drum)
- [GIF] Modular (Point orbit under the action of the modular group)
- [GIF] Release (Flapping triangular grid)
- [GIF] Inertia (Distorted grid)
- [GIF] Step Forward (Volume-by-slices animation)
- [GIF] Gridded (Associate family of Scherk's surfaces)
- [GIF] Running in Place (String art animation)
- [GIF] Reversible (String art)
- [GIF] Perpetual (Parallelograms with vertices traversing four circles)
- [GIF] Recapitulation (Fourier series with fivefold symmetry)
- [GIF] Turn Yourself Around (Turning lines)
- [GIF] Making Tracks (Deformations of a spherical curve)
- [GIF] Left or Right? (Rotating Roman surface)
- [GIF] Stay Connected (Rhombus tiling deformation)
- [GIF] Group Work (Families of rhombuses)
- [GIF] Because It's There (Contour animation)
- [GIF] Stepper (Two tessellations)
- [GIF] Anything Goes (Quadrilateral tessellations)
- [GIF] Take Flight (Another Cairo tiling animation)
- [GIF] Flap (Deformations of the Cairo tiling)
- [GIF] Phoenix (Contours of a singular surface)
- [GIF] Closing In (Hexagonal tiling morph)
- [GIF] Interchange (approximate Fourier polynomials)
- [GIF] Bridges (Many Brownian bridges)
- [GIF] Twinkle (Pseudo-randomly located oscillators)
- [GIF] Coalesce (Deforming an isometric pattern)
- [GIF] Derange (Deforming a plain weave)
- [GIF] Come Back (Fun with the square)
- [GIF] Reveal (The torus in relief)
- [GIF] Cantellation (Cross sections of the 16-cell)
- [GIF] Triakis (Cross sections of the triakis icosahedron)
- [GIF] Pushed Around (a geodesic in pentagon space)
- [GIF] The Chase (real part of Klein quartic)
- [GIF] Enneper surface + an introduction