3. L-systems

A method for generating skeletons that resemble delta shapes is presented; it is based on L-systems and turtle graphics. In the following sections, there will be a brief exposition of previous works that generate river deltas, an explanation about L-systems and how they were adapted for generating delta skeletons, the presentation of graphic results and their discussion, and finally, the conclusions and future

Satellite images of river deltas from NASA GloVis database [8]. (a) Mississippi River and (b) Fly River.

Technology, Science and Culture - A Global Vision, Volume II

Within the procedural generation area, the only work that can produce river deltas, to the extent of knowledge of the authors, is that of Teoh [9]. The author presents a simple method where a river is first generated when it reaches the ocean; new land is generated in its mouth in an irregular semicircle shape. Random points of the new coast are then selected, and from those points, new distributary rivers run until reaching the original river mouth. This method is fast, but the resulting deltas are very limited and not capable of generating many of the river delta types. Other methods for the modeling of river deltas in computer systems, such as the one of Seybold [6], belong to geological simulations; therefore, they contain data about the terrain composition, slope, and other variables. The amount of data and their processing produces very realistic graphical results in terms of delta shapes, but the computational cost is considerable, and thus, these models are not suitable for procedural generation of virtual worlds. Finally, methods like that of Justić et al.

L-systems are quite versatile, and they have a wide array of applications. The work of Leitner et al. [11] is related to plant generation, but it is focused on another branching structure: the roots. They present and adapt a method that generated root

On the other hand, there are applications unrelated to vegetation, such is the case of the generation of video game levels [12]. The authors propose to pair the L-systems with grammar evolution to improve the variety of the generated levels. L-systems have also been used to generate cities [13]; the distribution of city blocks is done by the recursive subdivision of the system. Even generation of virtual creatures is proposed in [14]; this method is also paired with evolutive algorithms to

[10] are mathematical models of the delta behavior.

make changes to the generated creatures.

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systems depending on the concentrations of minerals in the soil.

research work.

Figure 1.

2. Related work

These systems are formal grammars with parallel rewriting that were originally designed to describe plant growth. The grammar G is formed by an alphabet V which contains the symbols that can be used, an initial state ω called axiom, and a finite set of generation rules P; this is G ¼ ð Þ V, ω, P .

Symbols are put together to form words. The set of words that can be generated by the system is denoted by V\*; the axiom could be a symbol or a word. The generation rules are applied to a symbol α, and the result is a word χ which is called the successor; in the case where there are no generation rules for a symbol α, the symbol is repeated as is when rewriting the strings. The rewriting occurs for each character in order; this produces a new word. The rewriting process is repeated for an arbitrary number of iterations. In this chapter, the used systems are deterministic, which means that each character could have only one rule at most; therefore, when having the same parameters, the results are the same for every execution [7].
