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Programming and evolving physical self-assembling systems in three dimensions

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Abstract

Being able to engineer a set of components and their corresponding environmental conditions such that target entities emerge as the result of self-assembly remains an elusive goal. In particular, understanding how to exploit physical properties to create self-assembling systems in three dimensions (in terms of component movement) with symmetric and asymmetric features is extremely challenging. Furthermore, primarily top-down design methodologies have been used to create physical self-assembling systems. As the sophistication of these systems increases, it will be more challenging to use top-down design due to self-assembly being an algorithmically NP-complete problem. In this work, we first present a nature-inspired approach to demonstrate how physically encoded information can be used to program and direct the self-assembly process in three dimensions. Second, we extend our nature-inspired approach by incorporating evolutionary computing, to couple bottom-up construction (self-assembly) with bottom-up design (evolution). To demonstrate our design approach, we present eight proof-of-concept experiments where virtual component sets either defined (programmed) or generated (evolved) during the design process have their specifications translated and fabricated using rapid prototyping. The resulting mechanical components are placed in a jar of fluid on an orbital shaker, their environment. The energy and physical properties of the environment, along with the physical properties of the components (including complementary shapes and magnetic-bit patterns, created using permanent magnets to attract and repel components) are used to engineer the self-assembly process to create emergent target structures with three-dimensional symmetric and asymmetric features. The successful results demonstrate how physically encoded information can be used with programming and evolving physical self-assembling systems in three dimensions.

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Acknowledgments

We would like to thank the two anonymous reviewers for their thoughtful and insightful comments.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Calgary, 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada

    Navneet Bhalla, Peter D. Vize & Christian Jacob

  2. Department of Computer Science, University College London, Malet Place, London, WC1E 6BT, UK

    Peter J. Bentley

  3. Department of Biological Sciences, University of Calgary, 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada

    Peter D. Vize

  4. Department of Biochemistry and Molecular Biology, University of Calgary, 2500 University Drive N.W., Calgary, AB, T2N 4Z6, Canada

    Peter D. Vize & Christian Jacob

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  1. Navneet Bhalla
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Correspondence to Navneet Bhalla.

Appendix

Appendix

The following is a list of the materials and methods for constructing physical components and their corresponding environment, as well as the physical experimental procedure (at level three, using the three level approach) for the programming and evolution experiments.

1.1 Component materials and methods

The materials, including tools, used for constructing components include:

  • Eden 333 Polyjet rapid prototyping machine

  • Vero Gray resin

  • Neodymium (NdFeB) disc magnets; 1/16″ × 1/32″ (diameter × height), grade N50

  • Magnetic pole identifier

  • Magnet placement tools

  • Vice; built from a PanaVise bench clamp mount, a PanaVise low profile base, and a PanaVise low profile head

  • Sharpie paint pens; oil based, fine point (colours: black, white, purple, yellow, green, and orange) and extra fine point (colours: red and blue)

  • Rhino3D version 4.0 computer-aided design (CAD) software

The method for constructing the components has the following eight steps:

  1. 1.

    Create the CAD files using Rhino3D for the magnet placement tool (specifications provided in Fig. 15) and for the components, based on the specifications in Fig. 16 and in association with the components’ shape space (to determine key, lock, and neutral information locations on each component, as well as any component interaction markers on neutral shapes adjacent to information locations).

    Fig. 15
    figure 15

    Magnet placement tool specifications (counter-clockwise from top right: perspective, top, front, right views), with all construction units in mm; note two magnet locations are shown at the top of the component (centre and corner), however only one magnet location should be used per tool (two locations are show here to reduce the number of technical drawings)

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    Fig. 16
    figure 16

    Component specifications showing the base component dimensions, key shape, lock shape, and interaction markers (counter-clockwise from top right: perspective, top, front, right views), with all construction units in mm

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  2. 2.

    Fabricate four magnet placement tools (two with a magnet in the centre, and two with a magnet in the corner) and the components using an Eden 333 Polyjet rapid prototyping machine with Vero Gray resin and the CAD files.

  3. 3.

    Insert three neodymium disc magnets in each magnet placement tool, to create one tool with magnetic north polarity and the other with magnetic south polarity (identify polarity using the magnetic pole identifier).

  4. 4.

    Paint the magnet placement tools, using the sharpie paint pens (blue for magnetic north and red for magnetic south), to complete the construction of the magnet placement tools.

  5. 5.

    Insert magnets into the components by first identifying the appropriate 5-magnetic-bit pattern for each key and lock, and then placing magnets on the appropriate magnet placement tool (two magnets for a key shape and three magnets for a lock shape) and using the vice to insert the magnets into the appropriate location in the 5-magnetic bit pattern (Fig. 17).

    Fig. 17
    figure 17

    Example of constructing a component during a vice press, and magnet placement tool (left) and component (right) inside the vice

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  6. 6.

    Remove the magnet placement tool and component from the vice and separate the component placement tool and the component (the extra magnet will dislodge and create an air gap on the component where the magnets were inserted; this follows the component physical encoding scheme for minimising key-to-lock error interactions provided in Table 3).

  7. 7.

    Repeat steps seven and eight until all magnets have been inserted into all the components.

  8. 8.

    Paint, using the sharpie paint pens, the magnets that have been placed in the components (blue for magnetic north and red for magnetic south) and any component interaction markers (refer to Fig. 4 to use the appropriate colours), to complete the construction of the components.

1.2 Environment materials and methods

The materials, including tools, used for constructing the environment include:

  • Trotec Speedy 300 Laser Engraver laser cutting machine

  • Acrylic sheet; transparent, 3 mm in height

  • Mill board; 0.8 mm in height

  • Screws; first type (5/8″ in length, pan head, 6-32 UTS, 18-8 grade stainless steel), second type (1/4″ in length, pan head, 6-32 UTS, 18-8 grade stainless steel)

  • Hex nuts; 6-32 UTS, 18-8 grade stainless steel

  • Glue; Loctite, regular, gel

  • Angle brackets; 1″, stainless steel

  • New Brunswick Scientific Excella E1 Platform Shaker

  • Adobe Illustrator Creative Suite 4

The method for constructing the environment has the following six steps:

  1. 1.

    Create the CAD files using Adobe Illustrator for the jar rack parts (Fig. 18).

    Fig. 18
    figure 18

    Environment parts for jar rack (from top left to bottom: bottom part A, bottom part B, top part A, jar sleeve, and side part), with all construction units in mm

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  2. 2.

    Fabricate the jar rack parts (two bottom parts a and b, two side parts, and one top part) using a Trotec Speedy 300 Laser Engraver laser cutting machine using mill board for the jar sleeve and acrylic for the remaining environment jar rack parts, and the CAD files.

  3. 3.

    Glue the three bottom jar rack parts together (bottom parts a both below bottom part b).

  4. 4.

    Construct the jar rack by using the screws, hex nuts, and corner braces to secure the bottom, sides, and top parts of the jar rack, and using the screws and hex nuts to secure the jar sleeve to the top of the jar rack.

  5. 5.

    Fold the overhang pieces of the jar rack sleeve over the holes for the jars in the top par of the jar rack.

  6. 6.

    Place the jar rack on the shaker (Fig. 19), and secure the jar rack to the shaker using the screw on the side of shaker’s platform (these screws are supplied with the shaker), to complete construction of the environment.

    Fig. 19
    figure 19

    Photograph of the environment with the jar rack secured to the shaker, and a jar with mineral oil containing components as an example (jars of mineral oil are used to finalise the component’s environment; details are provided in physical experimental procedure)

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    Fig. 20
    figure 20

    Jar configuration (top view) for the programming experiments (left, PEX1–PEX5) and the evolutionary experiments (right, EEX1–EEX3), where the labels is the figure correspond to the experiment numbers provided in Tables 5 and 8, respectively

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1.3 Physical experimental procedure

The materials required to conduct the physical experimental procedure include:

  • Graduated cylinder

  • Mineral oil; Rogier Pharma light grade

  • Stopwatch

  • Jars; VWR clear glass wide mouth, plastic lid with rubber liner, 500 ml capacity, 91 mm by 95 mm (diameter by height)

The physical experimental procedure, for both the programming and evolutionary experiments, has the following seven steps:

  1. 1.

    Create the CAD files using Adobe Illustrator for the jar rack parts (Fig. 19, specifications provided in Fig. 18).

  2. 2.

    Measure 325 ml of mineral oil using the graduate cylinder for each jar used in the programming experiments (five jars) and the evolutionary experiments (3 jars).

  3. 3.

    Place the jars of mineral oil in the jar rack (Fig. 20).

  4. 4.

    Randomly place the components for each experiment into the appropriate jar, and secure the jar lid.

  5. 5.

    Turn the shaker on by setting the speed to 32.5 rotations per minute, and start the stopwatch.

  6. 6.

    Stop the shaker after 20 min.

  7. 7.

    Record the state of each system.

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Bhalla, N., Bentley, P.J., Vize, P.D. et al. Programming and evolving physical self-assembling systems in three dimensions. Nat Comput 11, 475–498 (2012). https://doi.org/10.1007/s11047-011-9293-6

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