Mathematical illustration, generative art, and writing.https://gelada.github.io/https://gelada.github.io/projects/warped-reality/https://gelada.github.io/projects/warped-reality/A group exhibition at the Composite Gallery, MoMath, bringing together works by Edmund Harriss, Henry Segerman, Steve Trettel, Stepan Paul, Chaim Goodman-Strauss, Robert Fathauer, and Nico Belmonte. The show — described in the proposal as "Straight and curved: artifacts from an abstract world" — creates a wonderland of geometry whose pieces illuminate how geodesics behave on curved surfaces, how holonomy (the Gauss-Bonnet theorem) relates turning to curvature, and how surfaces can deform without changing their intrinsic geometry (Theorema Egregium). Harriss's contributions include: **Geodesic Boards** — twelve 6×12" cherry boards CNC-carved with surfaces and engraved geodesic paths, paired with an online calculator; **Holonomy Blocks** — three interactive pentagonal loop tracks with a movable rook that reveals how parallel transport accumulates turning on spherical (120°), flat (108°), and hyperbolic (90°) surfaces; **2-ply veneer Curvahedra models** — assemblies whose corner angles can be varied to redistribute curvature, showing how the Gauss-Bonnet theorem constrains the overall shape; and **Foam hyperbolic surfaces** — large brightly coloured flexible sheets with negative curvature. The exhibit is subsequently supported by the Simons Foundation for presentation at the 2026 International Congress of Mathematicians.Fri, 01 Aug 2025 00:00:00 GMThttps://gelada.github.io/projects/bridges-2025/https://gelada.github.io/projects/bridges-2025/Exhibited "Gradient of Grain" (2024)Mon, 14 Jul 2025 00:00:00 GMThttps://gelada.github.io/projects/misshapen-chaos/https://gelada.github.io/projects/misshapen-chaos/A series of six clay 3D-printed vessels on walnut bases, each encoding a different parameter of the logistic map as the equations are transformed into machine toolpaths for the printer. The surface of each vessel — from regular coiled rows at the base to chaotic bumps at the rim — traces the period-doubling cascade as the map bifurcates toward chaos. Created with Vincent Edwards and Jean Schmidt. Exhibited at Bridges 2025 (Eindhoven) and at the Création: Between Art and Mathematics exhibition at the Institut Henri Poincaré, Paris (April 2026).Thu, 10 Jul 2025 00:00:00 GMThttps://gelada.github.io/projects/holonomy-blocks/https://gelada.github.io/projects/holonomy-blocks/A large-scale interactive exhibit for the Museum of Mathematics (MoMath), New York, made with Henry Segerman. Three CNC-carved wooden surfaces — a sphere (positive curvature), a flat plane (zero curvature), and a pseudosphere (negative curvature) — each carry a metal rook that slides along rails carved into the surface. Moving the rook around a right-angled polygon and returning to the start, visitors discover that the rook has rotated: the angle of rotation is the holonomy, directly encoding the total curvature enclosed. The same rook design works on all three surfaces, making the comparison immediate.Sun, 01 Jun 2025 00:00:00 GMThttps://gelada.github.io/projects/algebraic-starscapes/writing/related-work/https://gelada.github.io/projects/algebraic-starscapes/writing/related-work/The mathematical context for Algebraic Starscapes — roots of polynomials, height functions, Mahler measure, Diophantine approximation, and the hyperbolic geometry hidden in the complex plane — plus work that has appeared since the 2022 publication.Thu, 01 May 2025 00:00:00 GMThttps://gelada.github.io/projects/intersections-summ-2025/https://gelada.github.io/projects/intersections-summ-2025/Group exhibition organised by the Seattle Universal Math Museum (SUMM) and the Mercer Island Visual Arts League, celebrating how mathematics and art reveal truths about the universe. Works shown include Gradient of Grain and Curvahedra pieces.Mon, 03 Mar 2025 00:00:00 GMThttps://gelada.github.io/projects/jmm-2025/https://gelada.github.io/projects/jmm-2025/Exhibited "Geodesic Boards" (2024) with Stephen J Trettel — six CNC carved cherry pieces exploring geodesics on arbitrary surfaces, paired with an online interactive calculator.Wed, 08 Jan 2025 00:00:00 GMThttps://gelada.github.io/projects/genuine-pretending/https://gelada.github.io/projects/genuine-pretending/A philosophical framework for mathematical art developed with Roger Antonssen and drawn from Moeller and D'Ambrosio's reading of the Zhuangzi.Wed, 01 Jan 2025 00:00:00 GMThttps://gelada.github.io/projects/interview-wheatley/https://gelada.github.io/projects/interview-wheatley/An Interview with Jon-Paul Wheatley of Jon-Paul's balls for MAA Focus.Wed, 01 Jan 2025 00:00:00 GMThttps://gelada.github.io/projects/jmm-2024/https://gelada.github.io/projects/jmm-2024/Exhibited "Gradient of Grain" (2023), a wood carving exploring the relationship between digital geometry and natural wood grain patterns.Wed, 03 Jan 2024 00:00:00 GMThttps://gelada.github.io/projects/conversation-with-daubechies/https://gelada.github.io/projects/conversation-with-daubechies/An edited conversation with Ingrid Daubechies on the role of play in mathematical research, published in the Math+Play guest-edited issue of MAA Focus.Mon, 01 Jan 2024 00:00:00 GMThttps://gelada.github.io/projects/geodesic-boards/https://gelada.github.io/projects/geodesic-boards/A set of CNC-carved wooden boards that make geodesic curves on mathematical surfaces tangible and touchable. Joint work with Steve TrettelMon, 01 Jan 2024 00:00:00 GMThttps://gelada.github.io/projects/geometric-flows/https://gelada.github.io/projects/geometric-flows/Placeholder for project explaining geodeisc flow and continued fractions with Pierre Arnoux.Mon, 01 Jan 2024 00:00:00 GMThttps://gelada.github.io/projects/gradient-of-grain-article/https://gelada.github.io/projects/gradient-of-grain-article/A short Art Department piece in MAA Focus describing the making of Gradient of Grain. The wood grain is treated as the natural geometry of the material — level sets recording the tree's growth — and the cuts follow the gradient direction perpendicular to it, which is also the cleanest direction to carve. An algorithm starting from the centre draws gradient lines outward, splitting them when the spacing grows too large; the wood is photographed, grain lines are traced, and the resulting network of paths is sent to the CNC machine.Mon, 01 Jan 2024 00:00:00 GMThttps://gelada.github.io/projects/gradient-of-grain/https://gelada.github.io/projects/gradient-of-grain/Carving gradient paths into the grain of a piece of wood. Featured in the New York Times (October 2025).Mon, 01 Jan 2024 00:00:00 GMThttps://gelada.github.io/projects/nervous-systems/https://gelada.github.io/projects/nervous-systems/An interview with Jesse Louis-Rosenberg and Jessica Rosenkrantz, founders of Nervous System for MAA Focus.Mon, 01 Jan 2024 00:00:00 GMThttps://gelada.github.io/projects/einstein-mad-hat-awards/https://gelada.github.io/projects/einstein-mad-hat-awards/Award plaques created for the Einstein Mad Hat Awards in 2023. The awards celebrated the discovery of the hat monotile, solving the einstein problemTue, 28 Nov 2023 00:00:00 GMThttps://gelada.github.io/projects/bridges-2023/https://gelada.github.io/projects/bridges-2023/Exhibited "Study for Mathemalchemy's lighthouse" (2022), a collaborative work with Emily Baker, Ásgerður Johannesdóttir, and Sabetta Matsumoto using the Zipform system.Thu, 27 Jul 2023 00:00:00 GMThttps://gelada.github.io/projects/barth-sextic/https://gelada.github.io/projects/barth-sextic/A physical sculpture of the Barth Sextic — an algebraic surface of degree six with the maximum possible number of ordinary double points (65). Winner of the AMS prize for best textile, sculpture, or other media.Fri, 06 Jan 2023 00:00:00 GMThttps://gelada.github.io/projects/jmm-2023/https://gelada.github.io/projects/jmm-2023/Exhibited "Barth Sextic" (2020), a 20 cm sculpture in ash wood and brass representing the sextic surface with the maximum number of double-point singularities.Wed, 04 Jan 2023 00:00:00 GMThttps://gelada.github.io/projects/dyslexia-research-mathematicians/https://gelada.github.io/projects/dyslexia-research-mathematicians/Analysis of personal narratives from research mathematicians with dyslexia, exploring the strengths and challenges of neurodiverse mathematical thinkers.Sat, 01 Jan 2022 00:00:00 GMThttps://gelada.github.io/projects/mathemalchemy/https://gelada.github.io/projects/mathemalchemy/A large-scale collaborative mathematical art installation conceived by Ingrid Daubechies and Dominique Ehrmann, combining contributions from over two dozen mathematicians and artists. The installation — a richly detailed miniature world celebrating mathematics — premiered at the National Academy of Sciences in Washington, D.C. in 2022 and toured the US and internationally through 2025. Featured in the New York Times (March 2025).Sat, 01 Jan 2022 00:00:00 GMThttps://gelada.github.io/projects/revealing-dimensions/https://gelada.github.io/projects/revealing-dimensions/A 42'×8' mural installed at the Tulsa Regional STEM Alliance's Headquarters.Sat, 01 Jan 2022 00:00:00 GMThttps://gelada.github.io/projects/counting-books-and-beyond/https://gelada.github.io/projects/counting-books-and-beyond/A survey of mathematical books for children, discussing how they open up deep mathematical ideas to young audiences.Fri, 01 Jan 2021 00:00:00 GMThttps://gelada.github.io/projects/bridges-2020/https://gelada.github.io/projects/bridges-2020/Exhibited "Barth Sextic" (2020) at the virtual Bridges conference.Sat, 01 Aug 2020 00:00:00 GMThttps://gelada.github.io/projects/hello-numbers/https://gelada.github.io/projects/hello-numbers/A counting book where math provides all the drama, with Houston Hughes and Brian Rea.Wed, 01 Jan 2020 00:00:00 GMThttps://gelada.github.io/projects/algebraic-starscapes/https://gelada.github.io/projects/algebraic-starscapes/The beautiful patterns that appear when algebraic numbers are plotted with sizes determined by complexity (such as functions of the discriminant), revealing geometric structure.Sun, 01 Sep 2019 00:00:00 GMThttps://gelada.github.io/projects/illustrating-mathematics/https://gelada.github.io/projects/illustrating-mathematics/Strengthening and making visible the role mathematical illustration has always played in mathematical discovery. Sun, 01 Sep 2019 00:00:00 GMThttps://gelada.github.io/projects/jmm-2019/https://gelada.github.io/projects/jmm-2019/Exhibited "Three minimal surfaces from one piece" (2018, lasercut Mylar).Wed, 16 Jan 2019 00:00:00 GMThttps://gelada.github.io/projects/geometry-walnut-grove/https://gelada.github.io/projects/geometry-walnut-grove/Paper and artwork exploring perceptualism in a mathematical art project. Joint with Carl Smith and Angela Carpenter.Tue, 01 Jan 2019 00:00:00 GMThttps://gelada.github.io/projects/triply-periodic-minimal-surfaces/https://gelada.github.io/projects/triply-periodic-minimal-surfaces/Three 3D-printed models of triply periodic minimal surfaces, the Schwartz P, Schwartz D, and Gyroid surfaces.Tue, 01 Jan 2019 00:00:00 GMThttps://gelada.github.io/projects/shifting-ammann/https://gelada.github.io/projects/shifting-ammann/A 52'×8' wall installation at Oklahoma State University showing an Ammann tiling pattern deforming continuously along the wall — the geometry shifts and morphs while preserving the non-periodic structure.Mon, 01 Jan 2018 00:00:00 GMThttps://gelada.github.io/projects/zipform/https://gelada.github.io/projects/zipform/A computation-and-fabrication system for creating curved architectural forms by zipping flat-cut pieces together. Developed with architect Emily Baker at the University of Arkansas, Zip-Form pairs mathematical formulations for parallel transport with a simple jig-based assembly process, enabling complex 3D curves from plasma-cut steel and basic tools. The work spans a permanent public sculpture, papers at AAG and IASS, and an ongoing collaboration on shape-optimised concrete formwork.Mon, 01 Jan 2018 00:00:00 GMThttps://gelada.github.io/projects/digital-manufacturing/https://gelada.github.io/projects/digital-manufacturing/Research into geometry-driven digital fabrication — bringing mathematical structure to bear on how things are made. Projects span cooperative multi-robot 3D printing with custom slicing software, the expressive potential of 5-axis waterjet cutting beyond standard manufacturing constraints, and the Zip-Form system for curved architectural elements. The unifying thread is using mathematical understanding of geometry to unlock fabrication techniques that are simultaneously more precise and more flexible.Sun, 01 Jan 2017 00:00:00 GMThttps://gelada.github.io/projects/tilings-handbook-chapter/https://gelada.github.io/projects/tilings-handbook-chapter/Chapter 3 in the third edition of the Handbook of Discrete and Computational Geometry (CRC Press, 2017), co-authored with Doris Schattschneider and Marjorie Senechal.Sun, 01 Jan 2017 00:00:00 GMThttps://gelada.github.io/projects/curvahedra/https://gelada.github.io/projects/curvahedra/A modular construction system based on the Gauss-Bonnet theorem — identical curved pieces that zip together without glue to form spheres, toruses, and other surfaces. Began as a paper puzzle, funded via Kickstarter in 2016, and became a commercial product at curvahedra.com. The same geometry underlies the Gearhart Hall courtyard sculpture and the Zip-Form fabrication system.Fri, 01 Jan 2016 00:00:00 GMThttps://gelada.github.io/projects/elevator-deformations/https://gelada.github.io/projects/elevator-deformations/Two dimensional parquet deformations built off non-periodic tiling patterns. They deform and transform around the elevator enclosures in Champions Hall at the University of Arkansas.Fri, 01 Jan 2016 00:00:00 GMThttps://gelada.github.io/projects/visions-of-the-universe/https://gelada.github.io/projects/visions-of-the-universe/A mathematical coloring book co-authored with Alex Bellos.Fri, 01 Jan 2016 00:00:00 GMThttps://gelada.github.io/projects/bridges-2015/https://gelada.github.io/projects/bridges-2015/Exhibited "P-adics in Motion" (2015) with Roice Nelson.Wed, 29 Jul 2015 00:00:00 GMThttps://gelada.github.io/projects/jmm-2015/https://gelada.github.io/projects/jmm-2015/Exhibited three works: "Sakura" (2007), "Oval with orthogonal lines" (2014), and "Three studies in CNC milling" (2014).Sat, 10 Jan 2015 00:00:00 GMThttps://gelada.github.io/projects/spira-gyroid/https://gelada.github.io/projects/spira-gyroid/A large-scale barn-raising at the 2015 Joint Mathematics Meetings, in which participants collaboratively assembled the Spira-gyroid — a physical model combining the geometry of a spiral with that of the gyroid minimal surface. Barn-raisings at JMM are events where mathematicians and the public build a large geometric structure together, with the assembly process itself as part of the work.Tue, 06 Jan 2015 00:00:00 GMThttps://gelada.github.io/projects/patterns-of-the-universe/https://gelada.github.io/projects/patterns-of-the-universe/A mathematical coloring book co-authored with Alex Bellos.Thu, 01 Jan 2015 00:00:00 GMThttps://gelada.github.io/projects/2d-crystals/https://gelada.github.io/projects/2d-crystals/Collaboration with physicist Salvador Barraza-Lopez applying discrete differential geometry to atom-thin crystalline materials. Especially how the geometry helps understand electric, optical and chemical properties.Wed, 01 Jan 2014 00:00:00 GMThttps://gelada.github.io/projects/woven-rings/https://gelada.github.io/projects/woven-rings/Wedding rings designed using permutation theory and braid mathematics, then realised in braided copper wire and cast in silver. The weave pattern — a cyclic permutation threading each strand through every position — was selected by systematically generating and exploring all possible braid cycles in code.Sat, 05 Jan 2013 00:00:00 GMThttps://gelada.github.io/projects/number-2/https://gelada.github.io/projects/number-2/A short story in the Mathematical Intelligencer that uses mathematical induction as its narrative structure.Tue, 01 Jan 2013 00:00:00 GMThttps://gelada.github.io/projects/parallelogram-tilings/https://gelada.github.io/projects/parallelogram-tilings/Joint with Dirk Frettlöh, showing the worms in parallelogram tilings, where parallel sides link must be infinite if the tiling has finite orientations.Tue, 01 Jan 2013 00:00:00 GMThttps://gelada.github.io/projects/pentagonal-domain-exchange/https://gelada.github.io/projects/pentagonal-domain-exchange/Self-inducing piecewise isometries with pentagons and heptagons.Tue, 01 Jan 2013 00:00:00 GMThttps://gelada.github.io/projects/improvising-mathematics/https://gelada.github.io/projects/improvising-mathematics/A report co-authored with Alex Fradera on integrating improvisational theatre into a University of Arkansas honours mathematics course.Sun, 01 Jan 2012 00:00:00 GMThttps://gelada.github.io/projects/magnetic-klein-quartic/https://gelada.github.io/projects/magnetic-klein-quartic/A physical model of the Klein quartic, a genus-3 hyperbolic surface tiled by 24 regular heptagonsmbuilt from neodymium magnets.Sun, 02 Oct 2011 00:00:00 GMThttps://gelada.github.io/projects/academic-prejudice-humbleness/https://gelada.github.io/projects/academic-prejudice-humbleness/A book chapter in a book about working beyond disciplines that gives a slightly naive, but personal, attempt to lay out my thinking. Reading it back I would not say it the same way, but it still captaures a lot of my thinking today.Sat, 01 Jan 2011 00:00:00 GMThttps://gelada.github.io/projects/from-oranges-to-modems/https://gelada.github.io/projects/from-oranges-to-modems/Part of a collection of articles in Nature on the unexpected impact of Mathematics.Sat, 01 Jan 2011 00:00:00 GMThttps://gelada.github.io/projects/tiling-typography/https://gelada.github.io/projects/tiling-typography/A series of four typographic studies placing classic typefaces over mathematical tiling patterns.Tue, 01 Jun 2010 00:00:00 GMThttps://gelada.github.io/projects/spirographs-3d/https://gelada.github.io/projects/spirographs-3d/An exploration of spirograph curves extended into three dimensions, with Richard GrimesThu, 14 Jan 2010 00:00:00 GMThttps://gelada.github.io/projects/sculpture-system-5/writing/construction/https://gelada.github.io/projects/sculpture-system-5/writing/construction/From Polydron prototypes and a CNC router at Fab Lab Iceland to a night installation on the Eldfell lava field — and a second build at the Newcastle Maker Faire.Thu, 23 Apr 2009 00:00:00 GMThttps://gelada.github.io/projects/sculpture-system-5/https://gelada.github.io/projects/sculpture-system-5/A sculpture system of hinged triangles to make deltahedra, joint with Richard Grimes.Wed, 01 Apr 2009 00:00:00 GMThttps://gelada.github.io/projects/how-shapes-fill-space/https://gelada.github.io/projects/how-shapes-fill-space/A popular mathematics article for iSquared Magazine to accompany an exhibit at the 2009 Royal Society Summer Science Exhibition.Thu, 01 Jan 2009 00:00:00 GMThttps://gelada.github.io/projects/bridges-2008/https://gelada.github.io/projects/bridges-2008/Exhibited three works: "16 Squares" (oil on canvas), "Nautilus and Conch" (laser-cut wooden tiles), and "Sakura" (inkjet on Washi paper, pattern using the Penrose tiling and substitution rule).Thu, 24 Jul 2008 00:00:00 GMThttps://gelada.github.io/projects/responsibilities-mathematicians/https://gelada.github.io/projects/responsibilities-mathematicians/Article in Mathematics Today arguing that mathematicians need to be engaged in how their subject interacts with the world. Tue, 01 Jan 2008 00:00:00 GMThttps://gelada.github.io/projects/bridges-2007/https://gelada.github.io/projects/bridges-2007/Exhibited three works: "Nautilis and Conch" (laser-cut wooden tiles, first example of Rauzy fractals using non-PV numbers), "Ammann Squares", and "Ammann Scaling" (both canvas prints exploring the Ammann-Beenker tiling).Tue, 24 Jul 2007 00:00:00 GMThttps://gelada.github.io/projects/flattening-functions-flowers/https://gelada.github.io/projects/flattening-functions-flowers/Studies when a Lipschitz function on an expanding circle map can be 'flattened', made Lipschitz-cohomologous to a constant, on a flower, a geometric structure formed by the closure of a pre-image selector's image. Mon, 01 Jan 2007 00:00:00 GMThttps://gelada.github.io/projects/logic-mathematical-writing/https://gelada.github.io/projects/logic-mathematical-writing/A course using informal logic to teach clear mathematical writing to undergraduate students, developed at Queen Mary, University of London.Mon, 01 Jan 2007 00:00:00 GMThttps://gelada.github.io/projects/bridges-2006/https://gelada.github.io/projects/bridges-2006/Exhibited "24 Nine-fold Stars" (2006), a print on canvas exploring the scaling symmetry of a substitution rule with 9-fold symmetry.Fri, 04 Aug 2006 00:00:00 GMThttps://gelada.github.io/projects/non-periodic-rhomb-tilings/https://gelada.github.io/projects/non-periodic-rhomb-tilings/Construction of a family of rhomb substitution rules for all dihedral symmetries in the plane.Sat, 01 Jan 2005 00:00:00 GMThttps://gelada.github.io/projects/tilings-projection-method/https://gelada.github.io/projects/tilings-projection-method/Research into the relationship between substitution rules and projection tilings.Mon, 01 Jan 2001 00:00:00 GMT