I am reading Godel, Escher, Bach, and recursion is one of the main topics the book discussed. Recursion is a pattern and never ends, or goes to infinite. ( EX. Bach’s Fugue, Escher’s stairs, Godel incompleteness theorem).
I remember there was a Fractal Artbook in my home, i used to flip through when i didnt want to study. I think Fractal Art is one of the most interesting recursion topics!
Fractal Art is a never-ending self -similar pattern across different scales, like the snowflakes (Koch Snowflake).
Today we will be using GGPLOT2 to draw a fractal!
Fractal Basicwe use complex plain to express fractals.
Z=(a+b∗i),i=sqrt(−1) Z=(a+b*i), i= sqrt(-1) Z=(a+b∗i),i=sqrt(−1)
General Recursive formula algorithm
the initial value is C, then we repeating the calculations!
ZN=Zn−12+C,C=a+b∗i Z_{N}=Z_{n-1}^{2} +C, C=a+b*i ZN=Zn−12+C,C=a+b∗i
library(ggplot2)
max_iter=25
cl=colours()
step=seq(-2,0.8,by=0.005)
points=array(0,dim=c(length(step)^2,3))
t=0
for(a in step)
{
for(b in step+0.6)
{
x=0;y=0;n=0;dist=0
while(n
Summary
Besides fun to look at the fractal artwork, it has practical applications. Such as fractal dimensions provide a solution to measuring the coastline (coastline Paradox).
Reference:
http://www.r-chart.com/2010/08/fractals-in-r.html
