OpenEuphoria

Fractal Landscapes

• Posted by Michael Packard <lgp at EXO.COM> Feb 05, 1998
• 778 views

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--655872-198744418-886746114=:3995

Fractal nuts:
Here's something.  This computes a 2d fractal height map for a landscape
and displays and overhead view and quickie 3dish view.
color.gif is the color palette.  Land.gif is a sample image.

When it gets done X[x][y] is the matrix of heights.
maxlevel determines the size of the matrix N=(2^maxlevel)+1

--------------------------------------------
--Fractal Landscape Generator version .1  --
--Copyright 1997 Lord Generic Productions --
--------------------------------------------
include get.e
include machine.e
include image.e
include graphics.e
include pic_load.e
atom seed,Arand,Nrand,GaussAdd,GaussFac
--atom x,y

sequence X
integer maxlevel,addition,i,N
--stage,
integer D,d
atom sigma,H,delta,max,min

-------------------------------------------
--initization of Gaussian random thingy
Nrand=4
Arand=1000
seed=1234
GaussAdd=sqrt(3*Nrand)
GaussFac=2*GaussAdd/(Nrand * Arand)
--set_rand(seed)
------------------------------------------
function Gauss()
atom sum
sum=0
for i = 1 to Nrand do
  sum=sum+rand(Arand)
end for
return(GaussFac * sum - GaussAdd)
end function
-------------------------------------------
function f3(atom delta, atom x0, atom x1, atom x2)
atom y,z
z=Gauss()
y=(x0+x1+x2)/3+delta*Gauss()
return(y)
end function
--------------------------------------------
function f4(atom delta, atom x0, atom x1, atom x2, atom x3)
atom y,z
z=Gauss()
y=(x0+x1+x2+x3)/4+delta*Gauss()
return(y)
end function
---------------------------------------------
maxlevel=7       --initial parameters
sigma=2.0
H=.5
addition=1

---------------------------------------------
atom k
min=time()
N=power(2,maxlevel)+1
delta=sigma
X=repeat(0,N)
  for o=1 to N do
  X[o]=repeat(0,N)
  end for

X[1][1]=delta*Gauss()
X[1][N]=delta*Gauss()
X[N][1]=delta*Gauss()
X[N][N]=delta*Gauss()

D=N-1
d=D/2

for stage= 1 to maxlevel do
  -- going from grid type I to type II
    delta = delta * power(.5,.5*H)
  -- interpolate and offset points
  for x=d+1 to N-d+1 by D do
     for y=d+1 to N-d+1 by D do
     X[x][y]=f4(delta,X[x+d][y+d],X[x+d][y-d],X[x-d][y+d],X[x-d][y-d])
     end for
  end for
          --displace other points also if necessary
  if addition then
    for x=1 to N+1 by D do
        for y=1 to N+1 by D do
          X[x][y]=X[x][y] + delta * Gauss()
        end for
    end for
  end if

  -- going from grid type II to type I
  delta= delta*power(.5,.5*H)
  -- interpolate and offset boundary grid points
  for x = d+1 to N-d+1 by D do
  X[x][1]=f3(delta,X[x+d][1],X[x-d][1],X[x][d])
  X[x][N]=f3(delta,X[x+d][N],X[x-d][N],X[x][N-d])
  X[1][x]=f3(delta,X[1][x+d],X[1][x-d],X[d][x])
  X[N][x]=f3(delta,X[N][x+d],X[N][x-d],X[N-d][x])
  end for

  --interpolate and offset interior grid points
  for x = d+1 to N-d by D do
     for y = D+1 to N-d by D do
        X[x][y] = f4(delta, X[x][y+d], X[x][y-d], X[x+d][y], X[x-d][y])
     end for
  end for

  for x = D+1 to N-d by D do
      for y = d+1 to N-d+1 by D do
        X[x][y] = f4(delta, X[x][y+d], X[x][y-d], X[x+d][y], X[x-d][y])
     end for
  end for

  if addition then
    for x=1 to N by D do
        for y=1 to N by D do
          X[x][y]=X[x][y] + delta * Gauss()
        end for
    end for

    for x=d+1 to N-d+1 by D do
        for y=d+1 to N-d+1 by D do
          X[x][y]=X[x][y] + delta * Gauss()
        end for
    end for
  end if

 D=D/2
 d=floor(d/2)
 end for
max=time()-min
puts(1,"time: ") ?(max)          --this tells how long it took to generate
?(length(X)*length(X))
min=255 max=0
for x= 1 to N do
for y= 1 to N do
k = X[x][y]
if k!=0 then k=((k/5)*128)+50 end if
if k<1 then k=1 end if
X[x][y]=floor(k)
if floor(k)<min then min=floor(k) end if
if floor(k)>max then max=floor(k) end if
end for end for
puts(1,"min: ") ?(min)
puts(1,"max: ") ?(max)

i=wait_key()
i = graphics_mode(19)
sequence temp
temp=read_gif("color.gif")  --this gets the palette
all_palette(temp[1]/4)
display_image({0,0},temp[2])
atom color
display_image({0,0},X)
for x=1 to N do
for y=1 to N do
if x=1 or x=N or y=1 or y=N then color=150 else color=X[x][y] end if
if color>255 then color=255 end if
 y]/10+1}})

pixel(color,{180+y-(x/5),50+(x/2)-X[x][y]/20})

end for
end for


i=wait_key()
if i='m' then i=save_screen(0,"land.bmp") end if
----------------------------------------------



--655872-198744418-886746114=:3995