GEOMORPH – Everything Changes When Mathematics Meets Art

“If we adopt a more open ended approach, we can explore geometrical space in new ways, and turn geometry into a medium of discovery” 

Exhibition: The first Geomorph exhibition was at The Leonardo in Salt Lake City, the city’s science and art museum, in October, 2012. Am now working on a new and permanent exhibition to open at the Leonardo.

GeoMorph presented a new approach to geometry – with HD animations, dynamic models, digital interactive animations, and printed media.

Geomorph’s geometries are dynamic – where everything moves and changes: (i) Space-efficient, close-packing spheres, transform into new clusters, generating new 3D structures. (ii) Polygons connect and rotate about each other to create amazing shape-changing forms. (iii) Geometrical lattices interact to generate an, almost, infinite number of designs and patterns.

Applications for these new geometries might be off-planet dwellings, new nano-structures, more energy efficient architectures, or new art and design forms.

Other dynamic geometries were also shown with presentations to show how geometrical ideas have evolved historically. I ran workshops and gave lectures to accompany the exhibition: (i) Shape Changing Geometries for Architecture, Math, and Science; Geometry Through  Time – looking at the cultural applications of geometry through time in art and architecture.

1. Close Packing Sphere and Lattice Animations of dynamic geometries – these art forms are all created using geometrical systems. See, the examples below and Posts for short extracts from a few of the many dynamic HD animations that have been produced. The short extracts below are in very low res and you have to imagine high res animations on a very large HD flat screen monitor! The first and third animations below are created with 2D lattices from close packing sphere arrangements. The second is a short extract from one sequence of close packing spheres as they transform from one packing into another along a two dimensional plane.

Press The Images Below To See Low Res Extracts / Examples:


2. Shape-Changing Polyhedra. These are a family of shape-changing structures that are modular, and where many will  infinitely interconnect in 3D space with the property that, if a force is applied to one part of a shape-changing structure, the whole transforms from one shape-change arrangement into another. The structures can be small or very large – large enough to walk into, see the image on the left below, or small enough to be micro or nano sized.

Press the next three images to see movie clips that show examples of shape-changing polyhedra. Shells 1, 2, 3 Examples / Extracts:


3. 3D Structures Based on Dynamic Close-Packing Sphere  Lattices. Of the other three-dimensional structures that will be exhibited some are based on lattice structures generated by the Dynamic Sphere Geometry I developed in the late sixties. See an example of a sphere lattice structure, below left, based on a phi sphere packing. Press the image, below center to see an article (PDF) about Nancy Stetson’s art studio in Boulder, Colorado, that  uses one of the close packing sphere groups generated by the Dynamic Sphere Geometry. The inner dome is based on a unique close packing of spheres, of whole number values, that focuses sound in unique ways to enhance perception. The original design also featured colored blinds to change the color of the light filtering into the room. The image, below right, shows one way in which lattices can be derived from close packing spheres.

4. Art pieces. These are large high resolution prints derived using geometrical systems -of geometrical designs some black line and some in color. Limited editions are available for sale. The two examples show nesting polygon arrangements.

5. Animations of images seen in Altair and Images designs. For examples of extracts from animations please see Posts.

Press The Images to see Animation Clips:

7. Section on “Geometry Through Time.” A visual presentation with workshops of geometrical systems found in various cultures through time – with a section on a possible new type of geometry for the future. See my latest book, ‘3D Thinking.’

8. Lectures / Workshops – on geometrical systems and how they were applied to art, architecture, and designs in the past – and how they might be applied in the future. Depending upon the audience the mathematics behind the various geometries can be shown.