1. Fractal Landscapes
- Posted by Michael Packard <lgp at EXO.COM>
Feb 05, 1998
-
Last edited Feb 06, 1998
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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
2. Re: Fractal Landscapes
At 10:21 PM 98/02/05 -0800, you wrote:
>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.
>
Wow! your's is really a 'something'... professional works...
i want to know if your code could be modified to generate SEAMLESS
image(top/bottom, left/right). i remember that a codes generating
simple 2-d lanscape was once posted on this maillist(several months ago).
at that time, the quality of the image generated was not very good,
however, it generated top/bottom, left/right seamless image.
Bye! from Lee woo seob.
3. Re: Fractal Landscapes
On Sat, 7 Feb 1998, Lee woo seob wrote:
> Wow! your's is really a 'something'... professional works...
Thanx.
> i want to know if your code could be modified to generate SEAMLESS
> image(top/bottom, left/right). i remember that a codes generating
> simple 2-d lanscape was once posted on this maillist(several months ago).
> at that time, the quality of the image generated was not very good,
> however, it generated top/bottom, left/right seamless image.
A strict fractal image couldn't be seamless because of the nature of
fractals, but the fractal data could be massaged once generated. You'd
have to mark off a transition area all the way around and average the
heights in that area with their couterparts on the other side to smooth
the transition. Either that or mirror the data which looks funny at high
altitudes. Normally I use Seamless Welder in the Kai Power Tools to make
my images seamless. For landscapes I usually just create a bigger data
set and use parts of it.
I'm now tinkering with the 3d perspective stuff. I'm using the standard
3d projection transform on the points to see how horrible the compute time
will be. The next stuff I'll put up will draw polygons, so you can see
the detail differences various maxlevel settings will give you. Should be
really slow I imagine. Then I'll re-develop the quickie 2d transforms
which should be an order of magnitude faster.
If someone can write an assembly routine for the 3d rotation transform,
let me know.
Michael Packard
Lord Generic Productions
