Emergence of L-Cellular Morphogenesis


Alain Lioret.

Arts et Technologies de l’Image. Université Paris VIII.

e-mail: lioretalain@hotmail.com




What's happen when cellular automatas meet L-Systems? This paper proposes several methods of implementations combining the rules of construction of cellular machines and L-Systems, with genetic, neuronal network, couplings up, translations of codes. These methods result in the morphogenesis of bodies, as well for their structure (shape) as for their functional aspect (neuronal network with driving, sensory neurones, balance, etc.).


For a very long time, the artists were inspired by forms of the nature to create works. Without going back up to the myths of the antiquity, we can quote notably the fundamental influence of Odilon Redon, in his series of pictures " Les Origines " [ 1 ] which already presents in 1883 some hybrid and surprising creatures. Also, Goethe likes the biology and more particularly the very particular theory of evolution of plants, with its work “La Métamorphose des plantes”. [2]. These works are moreover going to inspire the fundamental publications in this domain of Ernst Haeckel [ 3 ] (see figure 1) which is going to give the main lines of forms of the nature in the art, followed a short time later by authors as Martin Gerlach and Karl Blossfeldt [ 4 ].

Figure.1 Aspidonia. © Ernst Haeckel.

The currents based on the biomorphism and the biocentrism follow (a period which extends approximately the 30s in the 60s), with the intervention of some major artists of whom Hans Arp, Max Ernst, Paul Klee, Pavel Filonov, Kazimir Malevich, as well as French Jean Fautrier, Brassai, and Wols. [5]. It will be followed by the movement Eco-Art of the 60s.

More recently, with the arrival of the computer as the working tool for the artists, creators' new generation appeared. After the fascinating discovery of fractals by Benoît Mandelbrot [ 6 ], new perspectives of the nature are born. Then, it is then the " breeders of art » that use evolutionists techniques of Darwin, adapted by Richard Dawkins [ 7 ] and his famous biomorphs.

Among the artists the most known in this category, let us quote, William Latham [ 8 ], Karl Sims [ 9 ], Steven Rooke [ 10 ] and Jeffrey Ventrella [ 11 ]. They are next at the same time to artists who use evolutionists or connectionists techniques to create beings endowed with artificial life.

This last one is an emergent domain in the years 80/90, and is exactly situated on the border of the sciences and the art, on the heart of problems connecting creativity and cognition. We can quote notably the works of Yoichiro Kawaguchi [ 12 ] or Michel Bret [ 13 ] (see figure 2) which breathe an art nouveau, where the morphogenesis is used without being really quoted: the new forms of the life such as she could be make their appearance.


Figure 2 : Hybrid Creature created by Michel Bret

1. Cellular Machines

In the vast field of tools implemented by the applications of the artificial intelligence, the cellular machines are a part of the first ones to appear, notably with the famous game of life proposed by Conway [ 14 ]. Tools abound and the models of cellular machines diversify with great names which strangely advance the domain, as Stefen Wolfram, with its work « The New Kind Of Science » [15].

Naturally, certain number of artists bends over their use and try to bring to the foreground it of new styles of works. Let us quote for example, Paul Brown [ 16 ] naturally, who is interested in this domain dices the 70s, but also Scott Draves [ 17 ], Erwin Driessens and Maria Verstappen who take out of real 3D constructions  [18 ] and Matthew Fuller who introduced the group Human Cellular Automaton [ 19 ].

2. L-Systems

At the same time another shape of language which is going to serve the intentions of news morphogenesis is invented by Lindemmayer [ 20 ]: it is L-Systems which allow to generate forms, in particular plants from recursively grammars. The results obtained with this type of techniques are excellent and obviously the artists, as Laurent Mignonneau and Christa Sommerer [ 21 ], Christian Jacob [ 22 ] among others are interested in these new modes of expressions, by coupling them very often with evolutionists algorithms to get closer some more to theories of Darwin, as proposes it Christian Jacob in combination with L-Systems.

3. Morphogenesis

We shall not return in this article on the impressive literature which exists in the definition of the techniques of morphogenesis. Let us quote simply the inspiration that we were able to pull works of D' Arcy Thompson [ 23 ] (see figure 3) and Rupert Sheldrake [ 24 ], thanks to his innovative theories on the “ formative  causality » and " morphogenetic fields » and the works of which are inescapable on the subject. The morphogenesis is a fascinating subject which brings big not yet resolute questions, it is a ground of magnificent experiment for the artists and the works presented here go to this direction.


Figure 3 :Morphogenesis by D’Arcy Thompson

4. Structure And Functional Aspect

Our comment does not however amount to researches on the structural morphogenesis only. Indeed, if the shape, and thus the aspect of the body are necessarily one of our major concerns, as artist presenting images, we are interested just as much in the functional aspect of the engendered creatures, which in our sense cannot be separated from the structural aspect.

It is moreover this difference which is very too present in the current realizations (the 3D characters, the first virtual actors), the visual aspect of which is already pushed to a very high degree, and even until photo realism. On the other hand, the functional part of the new creatures semi intelligent is there for the moment only at the experimental stage. It is true that mechanism of the life are so complex, that we are obliged to agree the use of simplified models, as that of the autopoiesis proposed by Maturana and Varela [ 25 ].

5. L-Systems With Cellular Machines

The originality of this work rests essentially on a use coupled by the cellular machines and the L-Systems. This experimental research ensues from a simple report: all the systems proposing realizations of virtual creatures (vegetable or animal) start generally at the stage of the assembly of components already realized, as the famous blocks or the sticks which we meet in the works of Sims (see figure 4), of creation of Golems, the software Framsticks (that we use in our works), etc.

The stage of development corresponding to the molecular chemistry is systematically jumped, what in our sense cannot help in the understanding of an original development.

Nobody having this day all the answers necessary for the development of the life, vegetable or animal, we can allow themselves as artist (unmistakable advantage on the scientists forced to prove what they advance) to experiment in new directions and show the results of hybrid creations.


Figure 4 : Galapagos. © Karl Sims

So, several methods of coupling up of the cellular machines with L-Systems are proposed. We quote here only those who began to give interesting results but many others are possible. The principle in every case is to use the rules of generation of cellular machines as function of chemical process, thus occurring in various stages of the physical morphogenesis.

Method 1: creation of whole landscapes with the cellular laws. This method consists simply in covering(marking out in squares) a 3D ground, and in using rules of cellular machines to place seeds of L-Systems which are thus going to survive and to be born according to very precise plans. Several levels of complexity are studied, according to the forms of used rules. The simplest are based on couples of vectors Survival / birth, on which we can grow variety of L-Systems in the places where the life is possible. More complex rules, with parameters of evolution of machines can even influence the grammars L-Systems which modify according to these parameters (for example states, generations, etc.) (see figure 5).

Figure 5. A cellular machine applied to the shoot of vegetation on a ground.


Method 2: form L-Systems modified by cellular machines. In that case, it is a question of using the cellular machines as generator of rules used in every recursive stage of the construction of L-System. That is that besides the usual grammatical rules used in these systems (among whom F to draw branches), we add the use of rules (A, B, C, etc.) which are in fact rules of classic cellular machines. So, in every new stage of the processes of creation, the cellular rules apply to the shoot of new branches / sheets / segments, according to the principles of survival and birth. This a little more complex method to be implemented presents the advantage to result in less predictable creations and thus more natural.

Method 3: genetic Coupling up of the rules of L-Systems with the rules of cellular machines. This method is possible only with certain forms of rules of machines (there are numerous variants there, we based ourselves on those presented in Mcell, the software of Mirek Wojtowicz [26]). Here, as well the rule L-Systems as the cellular rules are considered as phenotypes, and genotypes are built on the basis of binary multi parameterised coding. Even there, surprising results are obtained, even if a scientific justification of such a process is excessively difficult to operate. But, after all, the morphogenesis is indeed a very complex process which can be made only by combining in a very narrow way chemical reactions with physical evolutions (see figure 6).


Figure 6 : a creature plants created with the method 3

6. Cellular Morphogenesis

Besides, our researches also led us towards other uses of the cellular machines for the morphogenesis. So, in the same way as we used the rules of cellular machines to generate vegetation, we have them to apply to the construction of elementary forms, from Metaballs (or blobs). This very simple method allows to obtain various base forms, which we can consider either as members of the future creatures (for the structural aspect), or as functional organs of these creatures (muscles, sensory neurons for the touch, the smell, the sight, the search for balance, etc.).

The forms used as members are the simplest to generate and are build from basic rules of survival and birth of what we can consider as the essential cells of the alive bodies. Those created for the functional aspect can be generated only with rules more evolved in machines. To note that evolutionists experiments on populations of cellular machines were also used for this process.

7. L-System Morphogenesis

In the same order of idea, the grammatical rules of L-Systems were used to create creatures, vegetable or animal (not shall say rather about animat type), as for their structural aspect. This type of creation rather classic did not bring very innovative tracks in our system of creation, but to complete the organized realizations. It was especially one of the stages of test for the neuronal co-evolution applied to creatures, realized mainly with the software Framsticks. [27].

8. Neuronal Coevolution

One of the very important stages of our study on the morphogenesis takes place within the software Framsticks. It is about a simulator of artificial life very evolved and programmable, which allows to realize any sorts of experiments. We thus have it includes in our pipeline of realization to develop creatures, at the same moment in their structural aspect and especially in their functional aspect (network of neurons) (see figure 7).

Different populations of creatures realized with the various described methods higher were subjected to the evolutionist system of Framsticks. With various established criteria (speed, balance or simply aesthetics) we mimed the processes of large-scale evolution, what allowed to obtain original, autonomous creatures in their behavior, and capable of beings used for different basic tasks: run, catch a prey, run away, etc., and even dance!


Figure 7 : An evolved creature stemming from the process of creation

9. Realizations

From this creative plan, it is possible to take out various types of works, which are three types: fixed images, pre-calculated full of life images, real-time full of life images. Only this last category can really report the functional aspect of creatures, even if the quality of the real-time depiction does not allow to appreciate totally the structural quality which can be implemented with this system. It is for it that we also realized calculated works, with various types of depiction, to take advantage of a completely interesting pictorial morphogenesis.

Notably, we made certain trial number with methods of non photo realistic rendering, according to the principles exposed by Aaron Hertzman [ 28 ] for the video painting. Among the obtained realizations, these present the advantage to supply new styles of alive paintings, self organized and to create original pictures directly stemming from the artificial life (see figure 8). Furthermore, this method of work results naturally in new aesthetics of the movement, as described in [29].


Figure 8 : Another creature made with a non photo realistic technique, alive painting.


The originality of this system lies in the combination of techniques presented to build models of new morphogenesis. The rules of cellular machines and L-Systems had still never been used in this way. The main purpose was here to supply "patterns" of creation of life such as she could be, as describes it very well Fritjof Capra, in its work, the Web of the Life [ 30 ]. On the other hand, the opening of the system allows to obtain very different results of a visual point of view, what leaves to the artist the choice of a particular aesthetics, to present fixed or full of life images, even real-time.


I am more particularly anxious to thank Michel Bret for the inspiration that he my supplied and who allowed to see succeeding this work, as well as all the team of “Arts et Technologies de l’Image” (Université Paris 8) among which the enthusiasm and the creativity are precious.




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