Endless forms: Future of production

Introduction

This paper focuses on “endless forms” to use Darwin’s term in the above quote instead of “infinite variations” which is more familiar in architecture and design, and the term usually used for the examples presented here. The Darwin quote is to underscore the deep inspiration biology has provided for this ongoing body of work which includes industrial production of designed objects and sculptures, form in nature, and generative morphology of space structures. The latter is an ongoing work on mapping the morphological universe which I have termed the morphoverse, ² a hypothetical “universe of all possible morphologies.” ³ It is an interconnected ultra-massive higher-dimensional periodic table of form comprising periodic tables within periodic tables as an open-ended source for coding and generating the vast diversity of forms, structures, patterns, and designs. This paper focuses on industrial production as one application of generative morphology which underpins the morphoverse.

At the Surrey7-IASS conference in 2021, I presented four of the five Milgo Experiments (1997–2014)^4–7 on the collaborative work with the metal fabrication company Milgo-Bufkin. These are experiments in form and form-making carried out in a factory environment to make physical structures in sheet metal using digital fabrication methods. The experiments leveraged the exploratory spirit of the theoretical work in morphology toward applications in design, architecture, and art. Of the four experiments presented, this paper starts with AlgoRhythms, ⁴ Milgo Experiment 1 (Experiment 1, hereafter), and adds Experiment 5 on emergent designs and its spinoffs in art. This could not be included in the Surrey7-IASS presentation due to limitations of space and time. Both experiments, Experiments 1 and 5 , deal with mass-customization of architectural and design products and provide two different examples of “endless forms” in industrially produced designs. They exemplify the principles which translate digital form generation into the industrial production of physical objects, small and large, and can be applied to other products as well as space structures.

Triad of twins

The term “endless forms” appears in the closing sentence of Charles Darwin’s The Origin of Species and in the title of Carroll’s ⁸ book Endless Forms Most Beautiful. Darwin’s last sentence ends with two words, “being evolved,” and refers to evolution, an open-ended ongoing unfolding of beautiful living forms (living designs) from a simple origin. It is one of the two grand unifications in biology, the other being genetics. To a designer, biological evolution provides a premier example of how infinite designs can be produced, forever. It is an example of space-time design and production combining two twin phenomena, infinity-eternity and design-production. The infinity-eternity twin is the limit case of the space-time twin and design-production relates to the software-hardware twin. The design-production twin deals with principles, rules, codes and programs that underpin designs as the software component, and physical materials and methods that enable their translation as the hardware component.

With Evo-Devo, evolutionary developmental biology, evolution, and genetics have been united. This introduces a third twin, the unity-diversity twin, as part of nature’s design strategy. Unity, through a universal genetic code, and diversity through the recursive branching of the “tree of life” ⁹ which maps all living designs in one diagram. This triad of twins provides nature with a strategy which ensures that endless forms can be designed and produced forever. It is applicable to human-made designs and match the spirit of work presented here.

Endless forms in mass-customized production

The infinity-eternity twin drives the generative morphology aspect of the work (Lalvani^10–13) and deals with form-generation and form continuum within open-ended higher-dimensional frameworks which structure the morphoverse. The generative rules can generate endless forms forever in an ever-expanding higher dimensional space. The unity-diversity twin within this universe enables the generation of infinite design variations from a universal morphological code (morph code). Four examples of mass-customized designs through infinite variations which can morph from one to another in a continuum are shown here. They provide an example of a design strategy for industrial production of endless forms by adding the design-production twin to the theoretical work and complete the triad of twins.

Early example of mass-customization: AlgoRhythms

AlgoRhythms (1997–2004; Figure 1), the company’s trade name for a class of architectural products in sheet metal where curve-bending (curved-folding) was used to convert flat sheets into three-dimensional surfaces, provided the first opportunity to apply generative morphology to industrial production. Infinite variations in one material using one method of fabrication from an integrated morphological model were possible. Algorithmically generated curve-folded forms could be produced economically by folding single sheets within an industrial setting to manufacture architectural products—columns, wall, ceiling systems. Three-dimensional modeled developable surfaces, built from “building blocks”—the fundamental regions of the curve-folded surfaces—which could be morphed parametrically. This provided the morphological tool kit. The non-deformational bending of full metal sheets into curve-folded surfaces rather than building from separate parts that were joined led to a built-in economy of means. The algorithm (with Neil Katz) permitted continuous variations to adjust curvatures, lengths, and angles so one form could morph to others continuously with simple geometric transformations applied to the fundamental regions and replicated throughout the folded surface. Symmetric and asymmetric forms were enabled from the same building blocks. Our aspirations to go beyond non-deformational bending were not reached. Several ideas were considered at the time but were not realized. These included development of special tools and machines for folding, robotic sheet metal folding, and providing an interactive digital tool for designers to manipulate the parameters for their specific designs.

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Figure 1.

Full -scale prototypes of AlgoRhythm columns (1999–2003), 8–12ft tall, each from a single curve—folded steel sheet. The collection of columns in the factory environment (top) and eight individual columns (bottom).

AlgoRhythms was among the earliest examples of mass-customized products in architecture (Carpo ¹⁴ ). Applications were extended to curtain walls, undulating curved truss, curved undulated versions of “standard sections” and furniture ¹³ (p. 88, Figure C3).

A schematic diagram of a portion of the universe of columns mapped in higher-dimensional space is shown in Figure 2 to illustrate how form possibilities are visualized and displayed. Each direction in the diagram maps an independent variable (parameter) represented by an independent dimension in higher-dimensional space to define how each variable acts independently, or in interaction with others, and controls the geometry of a columnar structure. The diagram represents a multi-variable space and can be extended into a larger space by adding more variables. Within this microverse of columns, one column can morph continuously from one to another. The form continuum shows form in space is a frozen moment in time.

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Figure 2.

A universe of morphing columns with straight and wavy edges showing a form continuum mapped in hyper-cubic lattice space.

Mass-customization of emergent designs: Morphing Platters

As a sequel to the multi-parameter model of AlgoRhythms, this experiment (Milgo Experiment #5 (2010–2011)) called Morphing Platters ¹⁵ introduced a new automaton for emergent designs based on a single parameter, length. This length-automaton, or Lautomaton, is a geometric automaton. It is linear, hence one-dimensional, and divides any continuous curve in 2D or 3D space like a spiral or a line fractal (e.g. Peano or Hilbert curve) or any meandering line that files a plane or 3D space, into equal distances which provide the single control parameter. We showed this with a simple spiral, the Archimedean whorl. The Lautomaton (Figure 3; begun with Peter van Hage, and extended with Patrick Donbeck, both at Lalvani Studio) led to emergent designs shown here with dot patterns in stills from an animation. The starting image on the top left corner shows dots on a whorl while other images (reading from left to right) show the range of emergent patterns as the number increases. The dot patterns are obtained by changing the number shown with each pattern and representing the distance between two points on the whorl.

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Figure 3.

Stills from a pattern continuum of dots placed at equal distances on an Archimedean spiral controlled one number (shown on bottom right of each pattern) representing this distance.

The dot patterns were converted into its dual pattern, a Voronoi diagram, where each dot (vertex) was replaced by an area, a polygonal region, and the area converted into a hole. The edges of areas were converted into regions with a thickness which graded continuously from narrowest at the middle of the edge to the thickest at the vertex along a smooth curve to produce a rounded laser-cut hole. This converted the Voronoi polygons into curved voids and provided a way to extend digitally designed forms of AlgoRhythms to mass-customization of digitally emergent designs. It was applied to a simple product, a fruit platter in this instance, so it could be easily fabricated from flat sheets in quantity. The results were exhibit at Design Miami 2011 (Figure 4).

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Figure 4.

Fruit Platters in laser-cut steel from a display by Moss Gallery at Design Miami 2011 (top) and Moss Gallery NYC (bottom).

Each platter had a continuous surface with 300 holes. The range of patterns, surprisingly, included patterns with near global symmetry, asymmetry, spirals with 1 thru 8 arms, chiral cases, and so on. Symmetries, mirrored, and rotational, emerged in fleeting moments within asymmetry which was more prevalent. Of the thousand designs that were selected from a much larger set, 100 were physically built, each with its unique number. During the exhibit at Design Miami 2011, a video monitor showed the animation of 1000 platters from one to another, each with an associated number at the bottom of the screen. The number changed from 1 to 1000 in increments of 1 associating each design with a distinct number. The intended idea (but not realized) was for potential customers to stop the animation at a design they liked and provide us with a number. The number was to be sent to the factory which would fabricate the selected design and courier it to them the following day.

Within the context of industrial production, the Lautomaton led to five innovations.

One Control Parameter: First, it reduced the multiple parameters of AlgoRhythms to a single control parameter so infinite designs could be generated by changing a single number.

Emergent Designs: Second, it led to emergent designs, each different. This included patterns of different kinds (Figure 5) mostly without symmetry with startling appearances of mirror and chiral symmetries ranging from 1 through 8 in passing moments.

Morphing Voids: Third, each location of the dot, converted to a Voronoi void, led to designs of lightweight platters which could morph continuously from one to another.

Conservation of Mass: The voids morphed with (nearly) the same total void area (Figure 6), or conversely, the same “solid” area and hence mass. Each platter weighed (nearly) the same. The same amount of material (and voids) was being re-distributed over the same area, a demonstration of the principle of conservation of mass (and voids) in endless mass-customized designs. Our preferred goal was to achieve identical areas of solid uncut regions, but this required a more rigorous procedure for generating the curves than what we used.

Conservation of Cost: Fifth, each platter cost the same even though each had a different design. The variation in the production cost of different platters was within the permissible margin of cost variation for the manufacturer to declare them equal. All costs of making—material, preparation and set-up, shaping the curvature, finishing, and painting—were the same except laser-cutting which was expected to be different due to differences in the designs. It turned out, to our surprise, the laser-cutting cost was within the manufacturer’s margin. Since laser-cutting is a one-dimensional process, the cost of laser-cutting was directly proportional to the total cutting length and cutting time which includes stops and starts due to the voids. In this instance, all platters had 300 voids leaving cutting length as the principal difference. The analysis showed that the total cutting length, which equaled the total perimeter of all holes, fell within the permissible margin of variation. Here too, we wished we were able to perfect the geometry of voids, so their perimeters were exactly equal, an interesting example of perimeter-preserving endless designs. In industrial practice, an important point was made—mass-production and mass-customization became inter-convertible, and infinitely different designs could be generated at the same cost as identical designs.

Murray Moss, who presented the work at Design Miami 2011, captured the implications: “Each platter bore a pattern that was different form the one that came before and from the one produced after; the process did not produce any ‘economy of scale’ benefit, a cornerstone of the Industrial Revolution—meaning that there would have been no savings in cost had the process been programmed to produce identical patterns.” ¹⁶

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Figure 5.

Selected platter designs based on the concept in Figure 3 where each dot is converted into a cell as its topological dual.

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Figure 6.

Conservation of mass in the Morphing Platters series shown with 4 examples indicated with their void areas. Conservation of cost was determined by the manufacturer since the departures in the total perimeters of voids, hence cutting lengths and time of laser-cutting, fell within his permissible margin of deviation.

A fruit platter is a trivial object, but the experiment provided the principles which could be applied to larger more complex objects including space structures and architecture. Conservation of mass and cost are only two criteria among many others which can be added to guide design. Important extensions would be to apply this to 3D dimensional configurations and space structures where aspects like length, area, volume, weight, strength, density, etc. can be conserved within families of related structures which are distinct. A useful application in architecture would be mass-customized homes (or housing), each different in form, and having the same total surface area and weight, and built in the same amount of time with the same cost. Space frames provide another interesting example. Some examples of artworks in sheet metal are shown as extensions of this project.

Patterns based on GPS: Morphing88 (2014)

A commission from the NYC Metropolitan Transit Authority (MTA) provided an opportunity to design art panels for the 88th Street train station in Queens, New York. It required 24 art panels, 48″ x 36″, 12 on each on the eastbound and westbound platforms of the station. Morphing88 (Figure 7) adapted the algorithm used for Morphing Platters to the design of site-specific art panels and combined it with features of travel like continuous travel along a linear path year around. 365 openings in each panel along a continuous line starting from top left to the bottom right in a continuous wave-like winding path represented a year-round path. The path was angled to match the angle of the street to the equator. The pattern was specific to the GPS coordinates of the several streets served by the station and corresponding numbers were inscribed on the finished panels.

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Figure 7.

Morphing 88, an artwork where the automaton for platters is applied to the design of 24 art panels for a train station in NYC, 88th Street on the A line in Queens, where the distance between openings and angle in the patterns is based on GPS coordinates of the streets served by the station. (Photo credit: Bill Kontzias).

This artwork demonstrated that each point location on earth can have a specific pattern associated with its GPS coordinates, an idea that can be extended to other applications—architectural layouts, building exteriors like curtain walls, grids, screens, frit designs, etc.

Structures Based on Zipcodes (2017)

The idea of basing patterns on numbers was extended from GPS coordinates to zip codes in a sculpture competition. The sculpture ARCH 07201 (Figure 8, top left) was proposed for a ceremonial structure for New Jersey Transit Authority at the plaza of the train station at Elizabeth, New Jersey, based on its zip code 07201. And sculpture 12508 for Beacon, New York, based on its zipcode (top right). Site-specific structures could be designed for any town or city worldwide based on their postal codes which reach up to 12 digits. A 5-digit zip code has five elements as in these segmented structures (bottom), each in 10 states of rotation for digits 0 thru 9. This is another example of number-coded variations in design arts that can potentially produce endless forms. Other numbers—personal (numbers, dates, addresses, etc.), site-specific (coordinates as in Morphing88, altitudes, climate, etc.), data-based (economic, financial, population, census based, etc.), and others—could be used and tied to designs in 2D and 3D.

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Figure 8.

Two sculptures, 07201 for Elizabeth, New Jersey (top left), and 12508 for Beacon, New York (top right), based on their respective zip codes. 15 sculptures for different state capitals in the US, each a 5-segment structure representing the 5-digit zip code of state capitals, each segment representing a digit of the zip code (bottom).

Future of production

. . . the likelihood of two large snow crystals being identical is zero . . . Each winter there are about 1 septillion (1, 000, 000, 000, 000, 000, 000, 000, 000 or a trillion trillion) snow crystals that drop from the sky!. ¹⁷

In nature, the commonly accepted truism that no two snowflakes are alike applies across natural forms in the living and non-living worlds. “Nature is a supreme mass-customizer” ¹³ (p. 128) at all levels of scale from large molecules to genomes, organs to organisms, communities to ecosystems, and up its vast scale leading to galaxies and beyond. The three twin strategies—infinity-eternity, unity-diversity, design-production (software-hardware)—may be at work in nature to enable the making of endless forms. However, from the point of view of industrial production, there are three important distinctions between our physical designs and the unified diversity in living forms in nature.

First, the fundamental challenge inhibiting ubiquitous mass-customization at all scales in all processes and materials in industrial production is economy of scale, arguably the most important conceptual invention of the Industrial Revolution. For economic reasons, standard mass-production of identical copies of a product will continue as we design our industrially produced objects, from small objects to large structures. However, as shown with one example (Morphing Platters) earlier, digital means of production may help bypass economy of scale if the principle can be combined with design and generalized to other materials, sizes, and processes. This needs to be shown with different examples within different industries. Can the example of the proverbial snowflake, and other examples in nature, provide insights into methods that bypass economy of scale? The answer to this question must be yes for us to have any meaningful breakthrough in cracking the problem of economy of scale to enable mass-customization on a wide scale.

Second, the morphoverse comprises all possible forms, both physical and conceptual. This leads to two types of morphoverses with one essential difference. The conceptual morphoverse based on mathematical principles is infinite while the physical morphoverse, limited by the laws of physics and chemistry, is finite, hence smaller, however large it may be. The mathematical possibilities of snowflake shapes are likely to be larger than the physical ones. The number of physical productions by humans and nature are ultra-large but must be finite. Pure structures based solely on geometry and topology inhabit the mathematical morphoverse and are infinite in number. Physical space structures built using real materials inhabit the smaller physical morphoverse. Both morphoverses will drive the future of industrial production with the former providing the aspirational upper limit for the latter.

Third, another fundamental difference between living designs and our productions lies within the third twin phenomena, software-hardware. In biology, DNA (RNA) is software and hardware and the two are one. In human productions, software and hardware are two separate strands. In future this will change since biology promises to be the defining technology of the 21st century. The considerable exciting work in tying synthetic biology with architecture, design and building technologies (See, for example, works by Joachim Mitchell, Neri Oxman, David Benjamin, Rachel Amstrong, and others Alexandra Daisy Ginsberg suggests adding Synthetic Kingdom as a new branch to the three main branches of the tree of life.) will continue and accelerate. In a new scenario, number-coded shapes can be tied to natural genomes based on DNA or RNA via the equivalence between numbers and DNA (The section “DNA and Number”’ in Lalvani ¹³ shows the conversion of number to DNA’s characters A, T, C, G. The equivalence between number and DNA is established by showing examples of numbers based on different systems—binary, decimal, 4-base, and 8-base numbers. Since numbers have been used to code form and space structures in Lalvani ¹² (pp. 7–240) and Lalvani ¹³ (pp. 270–339), this sets the stage for number-based shape-scripting using DNA sequences.) and will require the use of nature’s existing molecular-technologies to build and assemble. In this case, mathematical information will be transcribed into DNA base sequences by means not yet clearly known. When established, this could lead to DNA shape-scripting by designers by navigating the morphoverse or otherwise. The means for scaling up design from this nanoscale to the macro-scale of architecture will require breakthroughs not yet available.

Notwithstanding the fundamental differences between physical form and mathematical form and the separation of software and hardware, the three twin phenomena provide an integrated design-production strategy that will drive future production. The unity-diversity twin, driven by integrated morphological generators leading to diversified design options guarantees mass-customization in industrial production. The infinity-eternity twin that drives the infinite form variations in space-time, guarantees production for forever. The software-hardware twin is exemplified by the digital-physical components of human made production. Unified generative morphology provides a comprehensive strategy which will shape the future of production in the three corresponding areas. The morphoverse will provide an inexhaustible source for generating unique forms and structures forever. It is the source of “infinite infinities” of form ¹⁸ and provides the upper limit for design possibilities and future industrial production. The infinity-eternity and unity-diversity twins will continue to drive human creativity for as long as our species exists.

Production of physical form deals with another triad, the triad of form-material-process. In our productions, form, material, and process are developed in parallel and are mostly disconnected. Slowly and incrementally, we are heading toward an integration between these three aspects of physical form. In nature, this triad is united and co-operates in the production of endless forms, all related but unique, and the co-operation is likely contributing to an overall economy of production. Within this form-material-process triad, form possibilities are leveraged from the encompassing physical morphoverse. A similarly organized higher-dimensional universe of materials needs to be invented. This could possibly be an extension of the proposed 118-dimensional periodic table of compounds. ¹⁹ The parallel universe of processes, also anticipated to be higher-dimensional, awaits. Once developed, these three universes will need to be interconnected to provide an accessible universal tool for artists, designers, architects, engineers, technologists, scientists, and makers in all fields, to use it the way artists create new colors from three primary colors, or chemists invent new molecules and drugs from the same periodic table of elements. ²⁰

The availability of a fully integrated universal form-material-process tool will provide an unending source for designing and producing endless forms within the human enterprise requiring our physical production tools and methods to change substantially. This will mark the upper limit of industrial production, something we are unlikely to reach but can aspire toward. This aspiration will drive our creativity forward, hopefully in harmony with nature which achieves the same.