Synthetic Plants

Anatomy of Form

Figure: 2D iterations of L Systems using genetic algorithms, An introduction to Lindenmayer systems

Aristid Lindenmayer, Hungary 1968

Aristid Lindenmayer first created l systems in 1968 to observe plant cell behavior and model plant growth processes in the development of multicellular organisms. A specific way of modeling gave way to a particular formal language, and within it, a formal grammar now called L Systems or Lindenmayer Systems (Figure 2)48. Formal languages, like L systems, contain “strings” of words taken from letters of a formal alphabet like A, B, C, for example. A formal grammar are sets of rules to produce within the formal language. These existed in mathematics and computer science before L Systems, now an essential part of formal language theory. It’s also classified as a parallel rewriting system because of its behavior when L Systems branch out into a tree-like structure by using a set of strings within the formal language49. The sets are used to create a tree-like structure in a computer environment, with different rules creating an other tree.

Aristid Lindenmayer was a Hungarian biologist and botanist who taught at the University of Utrecht and headed the theoretical Biology Group. As a biologist, he worked with organic materials and bacteria, especially the algae cyanobacteria Anabaena catenula. While working with the algae, he proceeded by creating a formal description of the simple algae’s development and its neighboring relationships between cells. To form the language, he generated infinite sets of strings. Strings are a collection of rules that produce and expand every symbol into a larger string. The tree’s construction starts from an initial axiom and a mechanism that translates the string into a geometric structure of lines, each getting smaller as it generates. As L Systems are part of formal language theory, which is made of words, it comes with a one-dimensionality or linearity, but this isn’t what L Systems follows50. Instead, the power lies in the use of trees, and graphs, nonlinear objects to show the possibilities in modeling with the L Systems.

Lindenmayer created the L System to be best used to provide a framework that can mathematically specify multiple biological hypotheses that can provide logical conclusions. However, the rulesets create assumptions about plants’ growth patterns. What needs to be noted is the system’s cellularity, which is the most basic part of the organisms that control local mechanisms51. This cellularity is used to represent larger plant modules repeated throughout the living organism.

The rules of the L System are applied iteratively, starting from the beginning state. The power is in how many rules it can apply to each iteration simultaneously, which differentiates the L System from other formal languages (applying one rule per iteration}. When applying its rule sets, it is strict and context-free, only applying to individual symbols. Although, when a ruleset is applied to the individual symbol and its neighbor, it is a context-sensitive L System. However, if the system produces one for each symbol, the system is deterministic, usually context-free L Systems commonly named D0L Systems. If, instead of one iteration, there are more than one, it is said to be a stochastic L System52 .

There are many different classes of L systems, one of the simplest being the D0L system. In this case, all symbols are nonterminals, which means each can be rewritten by the system’s ruleset creating a single production per nonterminal.

A | AB B | A

The axiom of the sequence is A Then the sequence follows:

A AB ABA ABAAB ABAABABA …

In this sequence, each part is a set of strings, together making up the language. Meanwhile, each string’s length gets sequentially smaller provided by the growth function in the set language. As a tree form, it can be seen in Figure 7, starting with B as the axiom of the sequence.

Each capital letter within the system has its own meaning. L is for parallel rewriting of nonterminals simultaneously. The 0 character means the information between letters or cells is zero-sided. The P means it’s propagating, never on the right side of the rule. D represents the system is deterministic, and there’s only one rule per configuration53. The capitals would be found in the name of the system; for instance, D0L Systems, as shown in the example above, are parallel writing, deterministic, and the information within cells is zero-sided.

Initially, L Systems were created to model living organic structures. However, it has been majorly applied to non-living specimens and applications like computer graphics depicting imaginary life forms, imaginary gardens, among others. L Systems are ultimately suitable to model artificial life because of their flexibility and simplicity towards rule changes. All these qualities made it possible to model parallelism, meaning parallels to actual life. Other similar models like cellular automata aren’t as flexible, so it’s not as easy to affect growth or create alterations within the species. Although, with L Systems, there’s still a lot of post-editing needed to model real specimens since the systems are still too simple54. In turn, some of these L Systems’ similar sidedness creates the perfect grounds to describe fractals with it.

The L Systems makes it possible for people without a computer science background to manipulate to their advantage. In the case of architecture, could these be applied to architectural structure or form? Structural systems now with space trusses, among others, seem to be very close in sequence to an L System as a first example. Right now, the simplest forms architects can incorporate are mapping schemes and visualization. As the system is also suitable for parametric design, this can also be incorporated into facade design on architectural buildings or interventions. As algorithms can show great detail, as, the Digital Grotesque Grotto interior by using technological capabilities like 3D printing and robotic fabrication, architects can start minimizing the amount of material used and still keep structural integrity. The L System creates an overall suitable environment to test out possibilities even outside of the computer science field.