Example Sierpiński triangle

[krzysztof]

I've always wondered how the AND operator works in this case:

'Sierpinski
graphic #Sierpinski, 200, 200

for x = 0 to 127
 for y = 0 to 127
  if (x and y) = 0 then #Sierpinski set(x, y)
 next y
next x

render #Sierpinski
end

Probably it is one of the best known codes for Sierpiński triangle. The similar program (operator AND) works fine under FreeBASIC, but not under Quite BASIC. Strange, isn't it?

[krzysztof]

Example of program that can draw the Sierpinski triangle using iterated function systems (en.wikipedia.org/wiki/Iterated_function_system). I'm not entirely happy with the used subroutines and arrays, maybe they can be improved?

'Sierpinski triangle, IFS
graphic #Sierpinski, 500, 500

x = 0
y = 0

for i = 1 to 100000
j = rnd(1)
if j <= 0.33 then call array1
if j > 0.33 and j <= 0.66 then call array2
if j > 0.66 then call array3

x1 = array(1) * x + array(2) * y + array(5)
y = array(3) * x + array(4) * y + array(6)
x = x1

#Sierpinski set(250 * x, 250 * y)
next i

render #Sierpinski

end

sub array1
array(1) = 0.5
array(2) = 0
array(3) = 0
array(4) = 0.5
array(5) = 0
array(6) = 0
end sub

sub array2
array(1) = 0.5
array(2) = 0
array(3) = 0
array(4) = 0.5
array(5) = 1
array(6) = 0
end sub

sub array3
array(1) = 0.5
array(2) = 0
array(3) = 0
array(4) = 0.5
array(5) = 0.5
array(6) = 0.5
end sub

[meerkat]

You may want to look at another solution to the problem.

This is a RB solution on Rosettacode..
rosettacode.org/wiki/Sierpinski_triangle/Graphical#Run_BASIC

Hope this helps..
Dan

[tenochtitlanuk]

I did an IFS example some time back- see my OLD website at atschool.eduweb.co.uk/taunton/LB/indexlb.html and find it near the bottom.
I love the way that random jumps create such 'organised' figures. First met it in Byte magazine years ago & programmed on other machines.

[krzysztof]

Thank both of You for the tips. The first concerns a completely different way of generating the fractal, but it is interesting too. Second, that the ifs system, just like in my program. I have read the code and I see that I can improve my one:

'Sierpinski triangle IFS method

graphic #Sierpinski, 500, 500

read j
p1 = 0

for i = 1 to j
 read a, b, c, d, e, f, p0
 a(i) = a
 b(i) = b
 c(i) = c
 d(i) = d
 e(i) = e
 f(i) = f
 p1 = p1 + p0
 p(i) = p1
next i

for w = 1 to 500000
 p2 = rnd(1)

 if p2 <= p(1) then k = 1
 if p2 > p(1) and p2 <= p(2) then k = 2
 if p2 > p(2) and p2 <= p(3) then k = 3

 'One can use instead:
 'if p1 <= p(3) then k = 3
 'if p1 <= p(2) then k = 2
 'if p1 <= p(1) then k = 1

 x1 = a(k) * x + b(k) * y + e(k)
 y = c(k) * x + d(k) * y + f(k)
 x = x1
 #Sierpinski set(250 * x, 250 * y)
next w

render #Sierpinski

end

data 3
data 0.5, 0, 0, 0.5, 0.0, 0.0, 0.33
data 0.5, 0, 0, 0.5, 1.0, 0.0, 0.33
data 0.5, 0, 0, 0.5, 0.5, 0.5, 0.34

[krzysztof]

Another version of random Sierpinski triangle, found in the Microsoft Small Basic manual.

graphic #Sierpinski, 600, 500
x = 1
y = 1

for i = 1 to 200000
 
 r = int(3 * rnd(1))
 ux = 150
 uy = 30
 
 if r = 1 then
  ux = 30
  uy = 1000
 end if
 
 if r = 2 then
  ux = 1000
  uy = 1000
 end if

 x = (x + ux) / 2
 y = (y + uy) / 2
 
 #Sierpinski set(x, y)

next i

render #Sierpinski

end