## Fractal

Moderator: nitrofurano

Posts: 770

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

### Fractal

Just for fun.

Incidentally, if I change the float types to fixed, it crashes. Has something gone wrong with fixed type maths?

EDIT: Updated with fixed and exit for, so if people use it here, they get the best version.

Code:
#define width 256
#define height 192

DIM x,y as FIXED
DIM xstart,xstep,ystart,ystep as FIXED
DIM xend,yend as FIXED
DIM z,zi,newz,newzi as FIXED
DIM colour as byte
DIM iter as uInteger
DIM col as uInteger
DIM i,k as uByte
DIM j as uInteger
dim inset as uByte

xstart=-1.6
xend=0.65
ystart=-1.15
yend=-ystart
iter=24

xstep=(xend-xstart)/width
ystep=(yend-ystart)/height

'Main loop
x=xstart
y=ystart

border 0
paper 0
ink 7
CLS

for i=0 to ( height -1 )/2 +1
for j=0 to width -1
z=0
zi=0
inset=1
for k=0 to iter
';z^2=(a+bi)*(a+bi) = a^2+2abi-b^2
newz=(z*z)-(zi*zi)+x
newzi=2*z*zi+y
z=newz
zi=newzi

if (z*z)+(zi*zi) > 4 then
inset=0
colour=k
exit for
END IF
next k

if NOT inset then
if colour BAND 1 THEN
plot j,i
plot j,192-i
END IF
end if

x=x+xstep
next j

y=y+ystep
x=xstart
print at 23,0;CAST(uinteger,i)*200/height;"%"
next i

BEEP 1,1
PAUSE 0

(This will take a long time. Even if you push an emulator to top speed)
Last edited by britlion on Sat Apr 07, 2012 10:41 am, edited 1 time in total.

Posts: 1488

Joined: Wed Nov 01, 2006 6:18 pm

Location: Santa Cruz de Tenerife, Spain

### Re: Fractal

Awesome!!!
I'll put this in the Wiki, if you don't mind, in the Examples section.

Posts: 770

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

### Re: Fractal

Course you can.

(Though again - why does it seem to break with fixed, not float?)

Posts: 770

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

### Re: Fractal

Oh - I also thought I should be able to use "end for" in the place I have "goto screen". Not sure why it refuses to compile that.

Posts: 1488

Joined: Wed Nov 01, 2006 6:18 pm

Location: Santa Cruz de Tenerife, Spain

### Re: Fractal

It might be a bug, or might be a matter of precision.
Don't know. I know there's an integer version of Mandelbrot, BTW.

Posts: 1488

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Location: Santa Cruz de Tenerife, Spain

### Re: Fractal

britlion wrote:Oh - I also thought I should be able to use "end for" in the place I have "goto screen". Not sure why it refuses to compile that.

The correct syntax for that is "EXIT FOR" (this is like a Break sentence in C/C++)

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Location: Kentucky US, used to be Birmingham UK

### Re: Fractal

quite nice

Posts: 770

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

### Re: Fractal

boriel wrote:
britlion wrote:Oh - I also thought I should be able to use "end for" in the place I have "goto screen". Not sure why it refuses to compile that.

The correct syntax for that is "EXIT FOR" (this is like a Break sentence in C/C++)

Doh! Me idiot.

Yes, that works. Much better than a goto.

Posts: 770

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

### Re: Fractal

boriel wrote:It might be a bug, or might be a matter of precision.
Don't know. I know there's an integer version of Mandelbrot, BTW.

I don't think a lack of precision should cause a restart, however...

And yes. I didn't do that one integer would be faster.

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Location: Slough, Berkshire, UK

### Re: Fractal

slenkar wrote:quite nice

Oh slenkar! Now you've given it away

Posts: 1488

Joined: Wed Nov 01, 2006 6:18 pm

Location: Santa Cruz de Tenerife, Spain

### Re: Fractal

britlion wrote:
boriel wrote:It might be a bug, or might be a matter of precision.
Don't know. I know there's an integer version of Mandelbrot, BTW.

I don't think a lack of precision should cause a restart, however...

And yes. I didn't do that one integer would be faster.

A restart???
Please send me the code. I would like to test it, please

Posts: 770

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

### Re: Fractal

Same code, with "FIXED" wherever DIM had "FLOAT"

I could believe in it going out of bounds or something, but shouldn't just crash...

Code:
#define width 256
#define height 192

DIM x,y as FIXED
DIM xstart,xstep,ystart,ystep as FIXED
DIM xend,yend as FIXED
DIM z,zi,newz,newzi as FIXED
DIM colour as byte
DIM iter as uInteger
DIM col as uInteger
DIM i,k as uByte
DIM j as uInteger
dim inset as uByte

xstart=-1.6
xend=0.65
ystart=-1.15
yend=-ystart
iter=24

xstep=(xend-xstart)/width
ystep=(yend-ystart)/height

'Main loop
x=xstart
y=ystart

border 0
paper 0
ink 7
CLS

for i=0 to ( height -1 )/2 +1
for j=0 to width -1
z=0
zi=0
inset=1
for k=0 to iter
';z^2=(a+bi)*(a+bi) = a^2+2abi-b^2
newz=(z*z)-(zi*zi)+x
newzi=2*z*zi+y
z=newz
zi=newzi

if (z*z)+(zi*zi) > 4 then
inset=0
colour=k
exit for
END IF
next k

screen:
if NOT inset then
if colour BAND 1 THEN
plot j,i
plot j,192-i
END IF
end if

x=x+xstep
next j

y=y+ystep
x=xstart
print at 23,0;CAST(uinteger,i)*200/height;"%"
next i

BEEP 1,1
PAUSE 1
PAUSE 0

Posts: 1488

Joined: Wed Nov 01, 2006 6:18 pm

Location: Santa Cruz de Tenerife, Spain

### Re: Fractal

It was a bug in Fixed multiplication.
I don't see much improvement.
Can you measure the time it takes to draw the fractal with fixed variables, please? There should be some performance gain.

NOTE: This release includes your MLDepacker routine (fastcalled).

NOTE2: Happy Birthday!

Posts: 770

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

### Re: Fractal

boriel wrote:It was a bug in Fixed multiplication.
I don't see much improvement.
Can you measure the time it takes to draw the fractal with fixed variables, please? There should be some performance gain.

I added a timer function to it, and grabbed the timer before and afterwards.

Float:
s777 : 5237.6 Seconds.
s789 : 5237.9 Seconds

Fixed:
S789 : 2159.76 Seconds

I think that's a fair speed improvement, actually....

boriel wrote:NOTE: This release includes your MLDepacker routine (fastcalled).

Nice! I added that to the library - so there's a link to the packer program in there too. You might want to tweak that to note that it's in the package.
boriel wrote:NOTE2: Happy Birthday!

Thankee Kindly. I'm /really/ getting old now!

Posts: 770

Joined: Mon Apr 27, 2009 7:26 pm

Location: Slough, Berkshire, UK

### Re: Fractal

Should be able to get it faster still using the integer method - which cheats and multiplies up decimals:

DIM xl,yl as long
DIM xstartl,xstepl,ystartl,ystepl as long
DIM xendl,yendl as long
DIM zl,zil,newzl,newzil as long

#DEFINE MULTIPLIER 10000

xstartl=xstart * MULTIPLIER
xendl=xend * MULTIPLIER
ystartl=ystart * MULTIPLIER
yendl=yend * MULTIPLIER
xl = x * MULTIPLIER
yl = y * MULTIPLIER

Though I tried this to abject failure. Anyone else get anywhere?