Example various fractals

[krzysztof]

I've always loved fractals. It is very interesting and exciting thing. On the site paulbourke.net/fractals there are many examples of different fractals with simple programs written in classic BASIC dialect. They can be easily converted into a RunBASIC. There is no sense to give too many examples, as they use rather simple, similar codes. Two examples are:

'Peter de Jong Attractor
'http://paulbourke.net/fractals/peterdejong/
graphic #deJong, 500, 500

x = 0
y = 0

for i = 1 to 100000
 x1 = sin(1.4 * y) - cos(-2.3 * x)
 y = sin(2.4 * x) - cos(-2.1 * y)
 x = x1
 #deJong set(120 * x + 250, 120 * y + 250)
next i

render #deJong
end

and

'Gingerbread man
'http://paulbourke.net/fractals/gingerbread/
graphic #Ginger, 500, 500

x = -0.1
y = 0

for i = 1 to 100000
 x1 = 1 - y + abs(x)
 y1 = x
 x = x1
 y = y1
 #Ginger set(40 * x + 150, 40 * y + 150)
next i

render #Ginger
end

[krzysztof]

Here is the Run BASIC version of my old program, first written in Turbo Pascal ages ago. It draws a graphical representation of the logistic equation with Lyapunov exponent.

'Feigenbaum bifurcation and Lapunov exponent

graphic #Bifurcation, 500, 500

x = 0.1

for r = 4 to 0 step -0.005

 s = 0
 for i = 1 to 200
  x = r * x * (1 - x)
  s = s + log(abs(r - 2 * r * x))
  #Bifurcation color("black")
  #Bifurcation set(100 * r + 50, -400 * x + 450)
 next i

 L = s / 200
 #Bifurcation color("blue")
 #Bifurcation set(100 * r + 50, 50 -50 * L)

next r

render #Bifurcation
end