Un fractal es una figura geométrica en la que, al fragmentarla (de aquí el nombre de fractal) se repite el mismo patrón una y otra vez. Os enseñaré 4 ejemplos muy típicos:
1.- Árbol Fractal: El patrón básico es una rama que se divide (con un ángulo concreto) en 2 mas pequeñas (se multiplica el tamaño de la anterior rama por un coeficiente menor de 1), y así sucesivamente. Aquí os dejo un ejemplo interactivo hecho por mí en el podéis jugar a variar el ángulo y el coeficiente:
2.- Copo de Nieve de Koch:El patrón básico es un segmento que se divide en 3 trozos iguales,sustituyendo el central por los dos lados externos de un triángulo equilátero con base el trozo sustituido.
Si partimos de un triángulo y aplicamos el algoritmo a cada uno de sus lados, en la siguiente animación podemos ver las 3 primeras iteraciones del proceso de construcción:
3.- Triángulo de Sierpinski: En este caso se juega con la superficie de un triángulo al que quitamos el triángulo inscrito en el centro, y así sucesivamente. Las primeras 4 iteraciones del algoritmo serían las siguientes:
4.- Conjunto fractal de Mandelbrot: Mas complejo que los anteriores, por lo que no entraré a explicar como se crea, pero si que os dejo un video increíble que hace un zoom en el que podemos ver la complejidad que tiene y cómo el patrón principal aparece recurrentemente:
¿Y sabeís que la naturaleza tiene sus propios Fractales? Aquí van algunos ejemplos:
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