program mandelbrot2;
{Second Mandelbrot Set drawer. This program extends the previous
one by including a limited zoom mode.}
uses crt; {A unit that allows us to read single keypresses.}
{Note to C programmers: the variable type "real" is equivalent
to the C type "float".}
var cx,cy: real; {Where do we want to center the brot?}
scale: real; {This is the "zoom" factor.}
limit: word; {Divergence check value.}
lp: word; {Convergence check value.}
a1,b1,a2,b2: real; {For calculating the iterations.}
x,y: integer; {The pixel we are drawing.}
ax,ay: real; {The actual position of (x,y) in relation to
the Mandelbrot set.}
key: char; {Dummy value for keypresses.}
procedure init256;
{Initialises a VGA mode 320x200 pixels, 256 colours. A little chunky
but the extra colours are worth it, and SVGA is beyond the scope of
this program.}
begin
asm
mov ah,0
mov al,$13
int $10
end;
{This is a little direct assembly language. Feel free to use this
routine, and the others that follow, in your own code.}
end;
procedure end256;
{Turns off the video mode and returns to standard 16-colour text mode.}
begin
asm
mov ah,0
mov al,$03
int $10
end;
end;
procedure pixel(a,b: word; c: byte);
{This procedure plots a pixel at screen coordinate (a,b) in colour c.
Again, there is no need for you to understand the intrinsic workings
of this routine - you are welcome to use it in your programs but do
be aware that silly values for a and b could cause unexpected results.}
var v: word;
begin
v:=a+b*320;
mem[$A000:v]:=c;
end;
procedure draw_brot;
begin
{Loop through all pixels on screen. For reasons that will become
clear, I am counting not from (0,0) but from (-160,-100).}
for x:=-160 to 159 do
for y:=-100 to 100 do begin
{What is the *mathematical* value of this point?}
ax:=cx+x*scale; ay:=cy+y*scale;
{And now for the magic formula!}
a1:=ax; b1:=ay; lp:=0;
repeat
{Do one iteration.}
lp:=lp+1;
a2:=a1*a1-b1*b1+ax;
b2:=2*a1*b1+ay;
{This is indeed the square of a+bi, done component-wise.}
a1:=a2; b1:=b2;
until (lp>255) or ((a1*a1)+(b1*b1)>limit);
{The first condition is satisfied if we have convergence.
The second is satisfied if we have divergence.}
{Define colour and draw pixel.}
if lp>255 then lp:=0;
{If the point converges, it is part of the brot and we
draw it with colour 0, or black.}
pixel(x+160,y+100,lp);
end;
end;
function getpix(x,y: integer): integer;
{Function that returns the colour of pixel (x,y). Basically
the Pixel procedure in reverse.}
var q: word;
begin
q:=x+y*320;
getpix:=Mem[$A000:q];
end;
procedure draw_cross(x,y: word);
{Draws a crosshair centered on (x,y), using XOR plotting.
See article for details!}
var i: integer;
j: byte;
begin
{Vertical line...}
for i:=-5 to 5 do begin
j:=getpix(x,y+i) xor 255;
pixel(x,y+i,j);
end;
{And horizontal line...}
for i:=-5 to 5 do begin
j:=getpix(x+i,y) xor 255;
pixel(x+i,y,j);
end;
end;
procedure select_point;
{A procedure which lets the user select a place to zoom in on.}
var xcross,ycross: integer;
{These are the x and y coordinates of our selecting crosshair.}
begin
{Put crosshair in middle of screen.}
xcross:=160; ycross:=100; draw_cross(xcross,ycross);
repeat
key:=readkey;
draw_cross(xcross,ycross);
{A neat thing about XOR plotting is that if you do it
twice, the second time restores the old colours!}
if (key='z') or (key='Z') then begin
xcross:=xcross-1;
if xcross<0 then xcross:=0;
end;
{Prevents the cross being moved off the display.
The same trick applies to the next three.}
if (key='x') or (key='X') then begin
xcross:=xcross+1;
if xcross>319 then xcross:=319;
end;
if (key='k') or (key='K') then begin
ycross:=ycross-1;
if ycross<0 then ycross:=0;
end;
if (key='m') or (key='M') then begin
ycross:=ycross+1;
if ycross>199 then ycross:=199;
end;
draw_cross(xcross,ycross);
{Redraw cross, in new location.}
until key=' ';
{When spacebar is pressed, start the zoom.}
cx:=cx+scale*(xcross-160);
cy:=cy+scale*(ycross-100);
scale:=scale/2;
{Shifts cx,cy accordingly and doubles the zoom level.
The picture is redrawn outside this procedure.}
end;
begin {Main section!}
{Set up video mode.}
init256;
{Set up initial values for drawing. Try compiling the program
with different values here if you like!}
cx:=0; cy:=0; scale:=0.02;
limit:=4;
draw_brot;
{Draws Mandelbrot set with initial values.}
repeat
key:=readkey;
{Takes a keypress from user.}
if key=' ' then begin
select_point;
draw_brot;
end;
{If spacebar pressed, user wishes to zoom in.}
until (key='Q') or (key='q');
{If Q pressed, user wishes to leave program.}
end256;
{Return to text mode.}
end.