Furniture Design Ideas

For the modeling of branching structures, L-systems have to be extended. The processing of the string sequence is now accomplished by means of a so-called pushdown automaton. This method contains the possibility to store, and at an­other time again to recall the state of the turtle in a stack. This occurs in such a way […]

Lindenmayer systems or L-systems, are one kind of string rewriting mecha­nism, consisting of a set of rules and symbols that model growth processes. An initial string or symbol, the axiom, is defined; one or more rules are added that replace the character string in a given alphabet. In an L-system, rules are executed in parallel: […]

The general mechanism of a rewriting system can best be illustrated with the so-called snowflake curve or von Koch curve. This curve is actually the classic example of a rewriting system, and, therefore, it is found in many places in the computer science literature. Rewriting takes place graphically: each edge of a given geometry is […]

Single Plants Are “Emerging” Aristid Lindenmayer’s approach to describing morphological forms of plants using so-called string rewriting systems [117, 118, 119] opened a broad sci­entific field in botany as well as in computer graphics. Text or string rewriting systems are subsets of rule-based systems, which have been analyzed for quite a while as solutions to […]

The number and variety of algorithmic methods that can be applied to model plants and in particular trees convincingly faithfully, is indeed surprising. It may be due to the relatively nonspecific structure of the botanical models that several good approximation procedures could be found. At the same time, the factual findings address the question of […]

In Sect. 3.4 we already mentioned the remarkable effect that the mathemati­cal method using the Golden Angle describes the arrangement of the seeds in many flowers very well, but that at the same time there is no indication of the biological emergence of these patterns. Actually, for the correct positioning of the seeds in correlation […]

The last procedural method discussed in this chapter generates climbing plants, which are actually in an entirely different category. Ned Greene [77] deals with the question of how the interaction of such plants with the environment and the incidence of light can efficiently be rendered, and at the same time how these plants can be […]

While these approaches, with the exception of the particle-based procedure of Reeves and Blau, endeavor to model trees as realistically as possible, it is the affirmed goal of Weber and Penn [231] to only find approximate, though realistic-looking solutions for tree modeling. Weber and Penn’s procedure re­quires a set of approximately 50 parameters, all of […]

Leonardo da Vinci assumed that for trees in a branch bifurcation, the cross­section of the father branch equals the sum of the cross-sections of his children. This was already discussed in Sect. 3.3. Likewise we already mentioned that this estimated value was proven to be amazingly precise. Figure 4.13 Tree model using strands: a) combination […]

In Sect. 3.2, we already addressed the Strahler analysis of trees and other net­works. Vannimenus and Viennot [222] extend this subject with the goal to find a combinatorial mechanism for the production of branching structures. Here, a randomly controlled algorithm is applied as well, though, in contrast to earlier procedures, the basis is a complex […]