Assembly Language – Jesse Colin Jackson’s Marching Cubes

The latest iteration of a decade-long investigation into modular construction systems in architecture (and beyond), Marching Cubes is a 3D-printed assembly system by the Canadian Artist Jesse Jackson. Inspired by the graphics algorithm of the same name, the project is a syntax for building volumes from 3D printed blocks. Thus far Jackson has trotted out his system twice: at a participatory ‘building party’ at the University of California, Irvine (UCI), and at a recent solo exhibition at Toronto’s Pari Nadimi Gallery.

A little history lesson is needed to appreciate Jackson’s blocks. In the late 1980s William E. Lorensen and Harvey E. Cline developed an algorithm for extracting a polygonal mesh of an isosurface from a 3D scalar field. Coming at computer graphics from a medical imaging perspective, their ‘Marching Cubes’ algorithm endeavoured to provide more accurate visualizations of CT and MRI scan data. The duo presented their findings at SIGGRAPH 1987 and published a paper shortly thereafter in Computer Graphics; in its abstract they summarized their method:

Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data [and] normalize it …

↑ The 15 cube configurations published by Lorensen & Cline in 1987; in 1995 an additional 18 were proposed by Evgeni V. Chernyaev, creating an ‘extended’ table of 33 configurations.

Since CT and MRI scans derive their three-dimensionality through a ‘multislice’ technique of stacked 2D scans – interpolation is of the utmost importance for image resolution. Lorensen and Cline’s technique calculated rows and columns of voxels from the 2D scan data and was particularly elegant in its translation of the organic contours of human physiology into smoothish surfaces. This ‘vocabulary’ of modular units with facetted, collinear exterior faces has served as building blocks for the construction of (representations of) the human form for decades.

↑ “The script is a custom C# component in Grasshopper for Rhino … it establishes a voxel grid around the input object; establishes where the boundary surface of the input object intersects with the vertices of each voxel; in any such intersection, it refers to a lookup table, and finds and outputs the appropriate block.”


↑ “Please help us build one of our test assemblies. Otherwise, interact as you see fit.” Participants in the Marching Cubes ‘assembly party’ at xMPL were given a blank canvas on which to build (photos: Tucker Moody).

Trained as an architect and an accomplished photographer, Jackson discovered the Marching Cubes algorithm through an ongoing research project into modular construction techniques and through a fascination with how pixels ‘construct’ images. Longtime collaborator Luke Stern (the head of Design Research at Vancouver’s Patkau Architects) assisted Jackson in developing a script (C#/Grasshopper) that translated any 3D form into an assembly of Jackson’s vocabulary of 21 blocks (ranging from a complete cube to a triangle-base pyramid) inspired by the Lorensen/Cline configurations. From there, the project moved from 3D modelling and noodling with geometry into fabrication. Jackson mobilized an army of students for a summer-long project to produce 1,500 blocks with 40 3D printers at the University of California’s Speculative Prototyping Lab. The bulk of each block is 1.75mm Natural PLA (printed with Printrbot Simple 3D Printers), 2.85mm coloured PLA faceplates (printed with Airwolf 3D’s Axiom and HD2X printers) codify surfaces that can be connected, and neodymium magnets embedded within the blocks facilitate connection.

Jackson’s next step: throw a party. He scheduled an event at UCI’s black box theatre, the Experimental Media Performance Lab (xMPL), and invited the public to come build. Simple instructions were provided (“Units are connected by matching the coloured faces. In a completed assembly, the coloured faces are all concealed inside.”), several shelves of neatly organized parts were available, a cold-rolled steel plate was laid out as a worksurface – and Jackson and other photographers were on-hand to document the results.


The second iteration of Marching Cubes was directly informed by the xMPL event – but this time the mandate was look rather than touch. At Toronto’s Pari Nadimi Gallery, Jackson constructed a 1.25 x 2 m ‘complete’ object based on the “most interesting” assembly developed by the participants in the October event. It features a pair of large right angle bases and slender legs (two copies of the same form, rotated 180°, sitting back to back) with jaggy protrusions and craggy crevices. In terms of assembly, there is a rhythm to the tolerances of 3D printing and the form wears its seams proudly. Likewise, a polychromatic grain emerges from the haphazard directionality of the blocks that is coloured by the faceplates within the volume.

It’s hard to imagine a more authentic exploration of the tension between digital representation and physical form than a sculpture about an algorithm. While process-oriented Jackson might bristle at the description of the work as sculpture – the video documentation of the xMPL event and the didactic ‘inventory’ of blocks that are prominently displayed by the gallery entrance are as much a part of the show as the giant form – it is undeniably sculptural. Questions of imperfect resolution notwithstanding, this much is certain: Marching Cubes is a decidedly digital intrusion into the material realm.

Jesse Colin Jackson
“Marching Cubes” is showing at Pari Nadimi Gallery (Toronto) through Jan 14