Pursuit of Emergence of Cultural Qualities from Algorithms

Satoru Sugihara, ATLV

Introduction

When we try to have a systematic way to think about designs, there are two major ways to take. One is to collect many existing designs, analyze them and categorize them into categories. Another is to start with an idea about a mechanism or a rule to generate design, expand it into more developed rules, and think about variations which can be generated with the rules. The first one then can build a design system through choices of categories and combinations of them. The first approach is inductive and the second is deductive. Generated results of the first system tend to be figurative and results of the second tend to be abstract. The first approach can be seen as humanistic and the second scientific. The first approach can deal with semantic issues and the second tends to deal with syntactic issues. Variations of results of the first tend to be discrete because they are generated through combinations of discrete choices. Variation of results of the second tend to be continuous because they are generated by applying the set of rules with continuous variations of parameters.

The first one can be called typological and the second one generative. The contrast of the two systems is obvious. But what is the relation between the two? Where did the existing designs which the typological system is based on come from? Existing designs in the human world are what people in the past or the present have made because of some reasons. Existing things in nature are what nature made through physical and chemical processes. Ultimately humans are made by nature and nature is made by atoms through some processes science have found and other processes science have not found. In this scientific view, a typological system is what a generative system could become ultimately. When rules in a generative system are sophisticatedly complex enough, continuous variations could start to show distinct diversity. Some of the results could start to show different qualities. This is what is called emergence. With emergence, syntax could deal with semantics, possibly like a node in deep learning neural networks starting to show a meaning through training such as the likelihood of cats. Pursuing these highly sophisticated and complex rules to generate designs which have emergent typological qualities is one of the most challenging and meaningful commitments which designers in our era can take.

This generative artwork research looks into this emergent relationship between a generative system and characteristics and qualities in cultural patterns. The author takes the weaving patterns of Atayal and Mapuche textiles as examples and seeks mathematical and geometric rules, i.e. algorithms to emerge cultural characteristics and qualities in generated 2 dimensional geometries and graphic images, produced on the Processing coding environment.

Agent-Based Simulation of Atayal and Mapuche Textile Patterns

As a first attempt, two types of textiles are analyzed: one in Atayal and another in Mapuche culture (figure 1, 2). Their geometric structure is analyzed in terms of procedural steps to draw the pattern such as when and what angle a line turns into the next line and when and how a line branches into multiple lines.

Figure 1 Diamond pattern of Atayal textile

Figure 2 Andean pattern of Mapuche textile

Then agent-based generative system to simulate the diamond pattern of Atayal textile and Andean pattern of Mapuche textile is developed. Figure 3 and 4 shows the results generated by the system.

Figure 3 Atayal diamond pattern agent simulation

Figure 4 Mapuche Andean pattern agent simulation

In the next process, the agent behaviors of simulating Atayal diamond pattern and Mapuche Andean pattern are integrated. Figure 5 shows the case when the diagonal lines of the nested Atayal diamond patterns start having stepping conditions like Mapuche Andean pattern. In those patterns, the nested diamond is treated as a module and each module has its own properties such as the angle and the size of the module, and the straightness of diagonal lines (straight diagonal line or horizontally and vertically stepping line). In figure 6, the modules start having various sizes, angles, and straightness. During the growth of those patterns as agents, when lines collide with other lines, those agents stop growing, avoiding intersections. In figure 7, it has various sizes and straightness, but the angles stay the same. In addition, it introduces horizontal line patterns which originally appear in the Atayal textile on the edge of the patterns.

Figure 5 Agents integrating Atayal diamond and Mapuche Andean pattern

Figure 6 Agents integrating Atayal diamond and Mapuche Andean pattern

Figure 7 Agents integrating Atayal diamond and Mapuche Andean pattern

The Atayal diamond has the meaning of eyes of ancestors. The horizontal lines in the Atayal diamond pattern represent the boundary between this world and the afterlife world where ancestors reside. The complex and organic patterns in Figure 6 could be interpreted as variety of groups of ancestors, showing the diversity of the rich heritage of the past instead of singular reading of the history. The self-organizing patterns in Figure 7, especially the distributed horizontal lines interacting with variety of the modules could be interpreted as ubiquitous presence and close relationship to the ancestors.

Generative Pattern Algorithms with Loose and Tight Rules

The textile pattern images #1–5 are generated by algorithmic rules. Those are experiments on how mathematical and algorithmic systems can start to obtain recognizable human cultural qualities, especially in Atayal culture in Taiwan and Mapuche culture in Chile. These algorithms are developed based on the analysis of Atayal and Mapuche textile patterns such as figure 1, 2, 8–13.

Figure 8 Atayal textile example

Figure 9 Atayal textile example

Figure 10 Atayal textile example

Figure 11 Mapuche textile example

Figure 12 Mapuche textile example

Figure 13 Mapuche textile example

Base Algorithm

Certain numbers of lines with a certain stroke weight are written in a rectangular area.
The lines are copied and rotated 180 degrees in the rectangular area.
The lines are mirrored horizontally.
The lines are mirrored vertically.
The lines are repeated in the X and Y directions.

Figure 14 The Base algorithm of textile pattern generation

Algorithm #1

A certain numbers of horizontal, vertical and diagonal lines with variable length are drawn in the base algorithm (a).

Figure 15 randomly generated patterns by the algorithm #1 part 1

Figure 16 randomly generated patterns by the algorithm #1 part 2

Figure 17 randomly generated patterns by the algorithm #1 part 3

Figure 18 randomly generated patterns by the algorithm #1 part 4

Algorithm #2

A certain numbers of horizontal, vertical and diagonal lines with variable length are drawn in the base algorithm (a) but if a new line is intersecting or touching with the already drawn lines, it is omitted.

Figure 19 randomly generated patterns by the algorithm #2 part 1

Figure 20 randomly generated patterns by the algorithm #2 part 2

Figure 21 randomly generated patterns by the algorithm #2 part 3

Figure 22 randomly generated patterns by the algorithm #2 part 4

Algorithm #3

Figure 23 randomly generated patterns by the algorithm #3 part 1

Figure 24 randomly generated patterns by the algorithm #3 part 2

Figure 25 randomly generated patterns by the algorithm #3 part 3

Figure 26 randomly generated patterns by the algorithm #3 part 4

Algorithm #4

A certain numbers of horizontal, vertical and diagonal lines are drawn in the base algorithm (a) but the lines cannot be open ended. The lines are either drawn to the edges of the rectangular area or closed as a loop. If a part of new line is intersecting or touching with the already drawn lines, the intersecting segments of the line is omitted.

Figure 27 randomly generated patterns by the algorithm #4 part 1

Figure 28 randomly generated patterns by the algorithm #4 part 2

Figure 29 randomly generated patterns by the algorithm #4 part 3

Figure 30 randomly generated patterns by the algorithm #4 part 4

Algorithm #5

In addition to the algorithm #4, a set of perpendicular short lines can be branched out from the existing lines.

Figure 31 randomly generated patterns by the algorithm #5 part 1

Figure 32 randomly generated patterns by the algorithm #5 part 2

Figure 33 randomly generated patterns by the algorithm #5 part 3

Figure 34 randomly generated patterns by the algorithm #5 part 4

The main difference in algorithms #1 to #5 is that the latter algorithms add more rules in addition to the previous ones making the algorithms stricter whereas algorithm #1 has more freedom and randomness. In other words, logics of algorithms of earlier numbers are looser, and the later ones are tighter. Although we don’t have a way to measure cultural qualities quantitatively, we can observe tendencies in our impression that the patterns generated by the algorithm #1 look geometric, i.e. mathematical and scientific, and towards patterns generated by algorithms #5, they start looking like what we would see in tribal textiles.

Discussion and Conclusion

In the results of the generated patterns, we see some glimpse of emergence of cultural qualities out of geometric rules implemented as computable algorithms in the generative design system. However, the exact relationships between the cultural qualities and the geometric rules are still up to discussion. One thing to point out is the relationship between the intersection avoidance rule and independence of graphical elements. When intersection of lines is prohibited, connected lines can be seen as an independent group of graphics, which we can recognize as a certain object. Then if we can imagine some meaning of the graphics of the object or see resemblance to existing objects in our world, we can recognize it as a symbol. Then what are the mechanisms and algorithms of forms of existing objects? In addition to this question, questions such as what kind of objects our culture uses as symbols, what is the relationship between mechanism of making and resulting forms in cultural artifacts are left for the future investigation.