Mandelbrot BASIC Program
Here's another cool bit of code to cut and paste into BASIC emulator.
Same as previous post: download and install a BASIC emulator onto your computer, and paste the code in. I used "PC-BASIC" made by Rob Hagemans because it is one of the few emulators that also emulates graphics! I got it off a site called SourceForge. A lot of BASIC/QBASIC/GW-BASIC emulators don't do graphics. PC-BASIC does. Worked for me on a modern Lenovo ThinkCentre desktop https://sourceforge.net/projects/pcbasic/
PC BASIC also one of the few emulators that seems to allow pasting lines of code in. That sure beats retyping everything. I typed this program into an email at some point. Then I just copied it in the email program like normal (Control + C) and pasted into into PC-BASIC by hitting F11+V and it all appeared. Then type RUN and Mandelbrot stuff appears.
There are an infinite number of fractions between any two whole numbers: between 1 and 2 there are 1/2, 1/4, 1/8, 1/1000, 1/2304049904, 1/9994848483292929, etc. The dark set are the Mandelbrot numbers. The colors are numbers outside the set, blasting toward infinity.
Zoom in for a closer look, and there is always a ton of similar detail to see: fractals!
Here's the code to cut and paste (remeber to use F11 + V to paste once you're inside PC BASIC):
10 DEFSNG A-Z
20 SCREEN 1: KEY OFF
30 MAXDWELL = 150
40 NUMCOLORS = 4
50 NUMROWS = 100
60 NUMCOLS = 100
70 YOFFSET = 1
80 XOFFSET = 1
90 INPUT "LOWER
LEFTHAND CORNER, REAL PART"; ACORNER
100 INPUT "LOWER
LEFTHAND CORNER, IMAG. PART"; BCORNER
110 INPUT "LENGTH OF
SIDE"; SIDE
120 CLS
130 COLOR 1
140 LINE (0, 0)-(NUMCOLS +
XOFFSET, 0)
150 LINE (NUMCOLS +
XOFFSET, 0)-(NUMCOLS + XOFFSET, NUMROWS + YOFFSET)
160 LINE (NUMCOLS +
XOFFSET, NUMROWS + YOFFSET)-(0, NUMROWS + YOFFSET)
170 LINE (0, NUMROWS +
YOFFSET)-(0, 0)
180 LOCATE 17, 1
190 PRINT "PERCENTAGE
COMPLETE = 0"
200 PRINT "DWELL FOR
LAST PIXEL = 0"
210 PRINT "LARGEST
DWELL = 0"
215 PRINT "MAXDWELL =";
MAXDWELL
220 PRINT "REAL PART
= "; ACORNER
230 PRINT "IMAGINARY
PART = "; BCORNER
240 PRINT "SIDE
= "; SIDE
250 HIGHDWELL = 0
260 GAP = SIDE / NUMROWS
270 AC = ACORNER
280 FOR X = XOFFSET TO
NUMROWS - 1 + XOFFSET
290 AC = AC + GAP
300 BC = BCORNER
310 FOR Y = YOFFSET TO
NUMCOLS - 1 + XOFFSET
320 BC = BC + GAP
330 AZ = 0
340 BZ = 0
350 COUNT% = 0
360 SIZE = 0
370 WHILE (SIZE < 4)
AND (COUNT% < MAXDWELL)
380 TEMP = AZ * AZ - BZ *
BZ + AC
390 BZ = 2 * AZ * BZ + BC
400 AZ = TEMP
410 SIZE = AZ * AZ + BZ *
BZ
420 COUNT% = COUNT% + 1
430 WEND
440 COLOR 1
450 LOCATE 18, 23
460 PRINT COUNT%; "
";
470 IF (COUNT% <
MAXDWELL) AND (COUNT% > HIGHDWELL) THEN HIGHDWELL = COUNT%: LOCATE 19, 16:
PRINT HIGHDWELL
480 IF COUNT% = MAXDWELL
THEN PSET (X, NUMROWS - Y + 1), 0 ELSE PSET (X, NUMROWS - Y + 1), COUNT% MOD
(NUMCOLORS - 1) + 1
490 NEXT Y
500 LOCATE 17, 22
510 PRINT 100 * X
/NUMCOLS; " ";
520 NEXT X
530 AS
= INPUT$(1)
Once you run it you'll be asked to input three numbers. Here's the starter version:
-2
-2
4
these three inputs will give you the same Mandbrot as above.
Other numbers suggested are:
-.114
.917
.017
You end up zooming into the Mandelbrot, but since it's like fractals it looks very similar (but never the same). Sort of like the chaos in the last post's bit of code.
You can zoom in too much and get crazy numbers like 1.2453245E-9 in the readouts. If you've got the time and computing power you can try this:
10 DEFDBL A-Z
This Mandelbrot code really grinds the hard drive as it works. I used the default 20 Line of Screen 1. You can up the ante for more colors and better resolution by changing the lines, same as last post. Each variation increases colors and/or resolution/and or size but always makes it take longer to actually render onscreen:
20 SCREEN 7 : KEY OFF
40 NUMCOLORS = 16
Lots more colors:
20 SCREEN 13 :KEY OFF
40 NUMCOLORS = 256
Here's one that gives you 16 colors but increases the image size from 100 rows and columns to 200:
20 SCREEN 9 :KEY OFF
40 NUMCOLORS = 16
50 NUMROWS = 200
60 NUMCOLS = 200
-2
-2
4
these three inputs will give you the same Mandbrot as above.
Other numbers suggested are:
-.114
.917
.017
You end up zooming into the Mandelbrot, but since it's like fractals it looks very similar (but never the same). Sort of like the chaos in the last post's bit of code.
You can zoom in too much and get crazy numbers like 1.2453245E-9 in the readouts. If you've got the time and computing power you can try this:
10 DEFDBL A-Z
This Mandelbrot code really grinds the hard drive as it works. I used the default 20 Line of Screen 1. You can up the ante for more colors and better resolution by changing the lines, same as last post. Each variation increases colors and/or resolution/and or size but always makes it take longer to actually render onscreen:
20 SCREEN 7 : KEY OFF
40 NUMCOLORS = 16
Lots more colors:
20 SCREEN 13 :KEY OFF
40 NUMCOLORS = 256
Here's one that gives you 16 colors but increases the image size from 100 rows and columns to 200:
20 SCREEN 9 :KEY OFF
40 NUMCOLORS = 16
50 NUMROWS = 200
60 NUMCOLS = 200
Like in the last post, if everything goes haywire, it's probably because your graphics card can't handle this program...even though it's like two decades later chaos, infinities, bifurcations and fractals use a lot of computing power. Plus, you're going through a BASIC emulator which is going to slow things down too.
How slow? Here's a video I took with Line 20 Screen set to only "1" and the colors limited to only 4. The little window is only 100 rows x 100 columns. Look how slow it goes!
How slow? Here's a video I took with Line 20 Screen set to only "1" and the colors limited to only 4. The little window is only 100 rows x 100 columns. Look how slow it goes!
