Self-organized 3D-Printing Patterns Simulated by Cellular Automata

Abstract

3D printers are usually used for printing objects designed by 3D CAD exactly, i.e., deterministically. However, 3D printing process contains stochastic self-organization process that generate emergent patterns. A method for generating fully self-organized patterns using a fused deposition modeling (FDM) 3D printer has been developed. Melted plastic filament is extruded constantly in this method; however, by using this method, various patterns, such as stripes, splitting and/or merging patterns, and meshes can be generated. A cellular-automata-based computational model that can simulate such patterns have also been developed.

Appendix: More Printed Patterns

Various patterns has been generated by the printing method. However, limited number of printed patterns are shown above. Other patterns are shown in this appendix.

1.1 Normal Stripes

Vertical stripes easily occur in simulation as described in Sect. 3.2, but they are rare in print results. However, they occur in print results by a Printrbot-Plus 3D printer (Fig. 13). They have never be seen in print results by the Rostock MAX. They can be reproduced; however, no exact set of conditions that makes vertical stripes is known.

1.2 Extinction of Stripes

Figure 14 shows an extinction pattern. (Fig. 15c also contains extinction examples.) The ellipses show extinctions. Because extinctions generate surplus filament, thick chunks of filament are seen at the top.

Fig. 13

Vertical stripe patterns. a PLA (by Printrbot Plus), b PLA (by Printrbot Plus)

Fig. 14

More extinction patterns (ABS, by Rostock MAX)

Fig. 15

More splitting and merging patterns. a ABS (by Rostock MAX), b PLA (by Rostock MAX), c ABS (by Rostock MAX)

Fig. 16

More wave patterns. a ABS (by Rostock MAX), b PLA (by Printrbot Plus)

Fig. 17

More mesh patterns. a ABS (by Rostock MAX), b ABS (by Rostock MAX), c PLA (by Printrbot Plus)

1.3 Splitting and Merging Stripes

Complex patterns can be more easily generated by using ABS (Fig. 15a, c). Figure 15c shows a pattern that contains extinction, split, and merge. The stripes at the top of this photo is very thick. Figure 15b shows a pattern generated using PLA, which seem to contain splitting, merging, and waves.

1.4 Crossing Waves

Wave-like patterns can be seen everywhere. Figure 16a is an example. However, a noticeable pattern shown in Fig. 16b is a combination of split, merge, and wave. At the center of this photo, stripes are split and merged. This pattern seems to propagate across the stripes.

1.5 Meshes

The mesh example shown in Sect. 4.4 contains thin meshes. More thick meshes can be observed in Fig. 17.