A fractal semigeométrico is an object whose basic structure, fragmented or irregular escalas.Muchas is repeated on different natural structures are fractal.
A natural fractal is a natural element that can be described by fractal geometry . Clouds, mountains, circulatory system, the coastlines or snowflakes are natural fractals. This representation is approximate, since the properties ascribed to the ideal fractal objects such as infinite detail, have limits on the natural world.
application was implemented to generate this type of fractal, using the L-System aqui una breve explicación
Un sistema-L o un sistema de Lindenmayer es una gramática formal (un conjunto de reglas y símbolos) principalmente utilizados para modelar el proceso de crecimiento de las plantas ; puede modelar también la morfología de una variedad de organismos. Los sistemas-L también pueden utilizarse para generar fractales auto-similares como los sistemas de función iterada .
Estructura de un sistema-L
La naturaleza recursiva de las reglas de los sistemas-L conduce a la autosemejanza y por tanto facilita la descripción type fractal forms . Plant models and natural-looking organic forms are easy to define: to increase the recursion level the form slowly grows and becomes more complex. Lindenmayer systems are also in generating polulares artificial life.
grammars, L systems are very similar to the semi-Thue grammar (see Chomsky Hierarchy ). L-systems are also known as the parametric L systems, defined as a set
- G = {V , S , ω, P}, where
- V (the alphabet ) is a set of symbols containing elements that can be replaced (variables )
- S is a set of symbols that contains elements that are stationary (constant )
- ω is a string of symbols V defining the initial state of the system (or start axiom )
- P is a set of rules or productions that define the way in which the variables can be replaced by combinations of constants and other variables. A production consists of two strings - the predecessor and successor.
grammatical rules of L-systems are applied iteratively from an initial state.
An L-system is context-free if each production refers only to an individual symbol and not their neighbors. When the application of a rule also depends on its neighbors, says the L-system is context sensitive .
The system is deterministic if there is exactly one production for each symbol. A deterministic L-system is context-free and generally referred to a system-L0D. When multiple outputs and each is chosen with a certain probability then it is a stochastic L-system.
- Well now we know that this is the fractal and the L, it was the deployment of an application which graphically, would help to generate any fractal DoL defined in the system.
Koch curve
A variant of the Koch curve using only right angles.
- variables: F
- constant : + -
- start : F
- rules: (F → F + F-F-F + F)
Here F means "draw forward", + means "around 90 ° to the left" and - means "around 90 ° to the right."
- n = 0:
F
- n = 1:
F + FF-F + F
- n = 2:
F + FF-F + F + F + FF-F + F-F + FF-F + F-F + FF-F + F + F + FF-F + F
- n = 3:
F + FF-F + F + F + FF-F + F-F + FF-F + F-F + FF-F + F + F + FF-F + F +
F + FF-F + F + F + FF-F + F-F + FF-F + F-F + FF-F + F + F + FF-F + F-
F + FF-F + F + F + FF-F + F-F + FF-F + F-F + FF-F + F + F + FF-F + F-
F + FF-F + F + F + FF-F + F-F + FF-F + F -F + FF-F + F + F + FF-F + F +
F + FF-F + F + F + FF-F + F-F + FF-F + F-F + FF-F + F + F + FF-F + F
Data is input to the program, also will choose the number of iterations
and the vector direction.
And the results are as follows:
The program is done in the MATLAB environment, using the M language, own it, the download link is this Fractals syntactic , the program code will be released in the coming weeks. Gerardo Ortega
Reaño
Computer Engineering National University of Trujillo
