THIS PROGRAM AND ARTICLE IS FOR THE SINCLAIR QL
INTRODUCTION
Welcome to the magical world of fractal geometry (“the mathematical study of forms having fractional dimension”). Fractal geometry has been used to build complex mountain ranges and “growing” plants by Lucas Films. It has also been helpful in the study of the baffling world of turbulence. This world was developed by Benoit B. Mandelbrot, a researchest at the IBM Research Center in Yorktown Heights, NY. The “numbers” which lie within the “fractal plain” are said to be within the Mandelbrot set (see solid black area in fig. 1). The set is created and explored by repeatedly calculating a set of complex, real and imaginary numbers. A complex number is any number of the form a+bi, where a and b are real numbers and i=square root of -1. A real number is one in which there is no imaginary part. An imaginary number is a complex number with b not equal to zero. (A full discussion of imaginary and complex numbers is beyond the scope of this article and knowledge of the author.) By using an iterative process, one can generate the Mandelbrot set. Numbers which do not “fly-off” to infinity are said to fall within the Mandelbrot set. This is where the computer comes in — the Number Cruncher! For high resolution, a maximum of 1000 iterations is required. In order to fit the resulting data into an unexpanded QL, I have chosen a low to medium resolution with an iteration of 255. If after 255 steps the calculated number does not equal 4, it is assumed to lie within the Mandelbrot set (see fig. 4 for example of the calculation).
The real beauty of fractal geometry is discovered by “zooming” into areas along the edge of the Mandelbrot set. An infinite number of “worlds” can be discovered. By assigning colors to the numbers that “fly” away from the set, one can find violent, yet beautiful, vortices (see figs. 2 & 3). One can also discover minature replicas of the parent set, along with drastic metamorphoses.
THE ADVENTURE BEGINS
To start your exploratory adventure into the Fractal World, you must first set the parameters of the search. (NOTE: As written, the program expects to be loaded and run from Microdrive #1. Use the command <LRUN mdv1_mandelbrot>.) The selection of “Define New Parameters” from the main menu will allow you to set your sights and the magnification scale needed for zooming into this magical world. First, set the starting corner for the search. A-Corner [real part] is the starting point along the x-axis of fig. 1, B-Corner [imaginary part] is the y-axis point. The size of the search is the length of the sides (a square starting at A & B-corner). When the length of a side is around .01025 or smaller, the resolution of the program begins to fall off. You will need to specify the device (microdrive, floppy disk, etc.) and a name for saving the resulting map. To keep the default device and/or name, simply press RETURN. (NOTE: Remember to include the underscore “_” when naming the device.) After checking to see if the information is correct, you are whisked off on your trek to that particular corner of the fractal world.
fig. 4
gap=side/200
for m=0 to 199
for n=0 to 199
real=n*gap+a_corner
imaginary=m*gap+b_corner
zr=0: zi=0: count=0
repeat loop
r=zr^2-zi^2+real
zi=2*zr*zi+imaginary
zr=r
size=zr^2+zi^2
if size>=4 then exit loop
count=count+1
if count>=255 then exit loop
end repeat loop
end for n
end for m
NOTE: Lines in italics are done via machine codeWhile the program is calculating and plotting the selected map, the ESC key will provide you with a report on the status and a mini-menu. The mini-menu will allow the saving of data in progress or a fresh start. (NOTE: Those which cannot operate their QL in F1/Monitor mode may miss the first 8 or so lines of the plotted set — the ESC key will keep you informed of your whereabouts.) When saving the data and screen, please be sure your device and medium is ready. If at any time you find yourself out of the program, due to an ERROR or by pressing BREAK, you can return by entering as a direct command <main_prog>. DO NOT Run the program, as this will clear the variables used to Call the machine code routines.
Once the computer has completed calculating all 40,000 points in the plane, a prompt will appear asking you to ready the device for saving. A directory of the device is provided, to help avoid overwriting data you may wish to keep. By answering “Yes” to the prompt, you can overwrite the files if you so desire. Another caution on saving: Insure that the medium will have enough space for all of the data, approximately 147 sectors total. The iterative mathematics is done via a machine code routine to avoid the days of computer-time which would be required by BASIC. If one were to calculate a fractal plane which lay entirely within the Mandelbrot set, a total of 71,400,000 calculations would be required.
fig. 5
SUGGESTED "HUNTING GROUNDS"
Real Corner Imaginary Corner Side
-2.25 -1.5 3.0 (see fig. 1)
-0.19920 1.01480 0.05227 (see fig. 2)
-0.95 0.23333 0.06667
-0.713 0.49216 0.22213
-1.781 0.0 0.013 (see fig. 3)
-0.75104 0.10511 0.01025
-0.74758 0.10671 0.00108
-0.74591 0.11196 0.00143
Once a completed picture and data of an area is stored, it can be recalled at any time by selecting “Load Screen and Data” option from the main menu. (Surprise! Surprise!) This option will also re-load a partially calculated plane, allowing one to continue development at a later time.
The color assignments which are provided as a default will not always provide a pleasing result. Therefore, option “Re-Define Color Data” provides a means to select a more satisfactory palette and distribution. Before re-coloring a map for the first time (or one that has just been loaded), the distribution of points must be calculated. It will take about 8 minutes to run through all 40,000 points. (NOTE: Once calculated, this data does not need to be re-calculated before re-defining the colors, as long as the current map is still in memory.) After this array has been amassed, the highest and second highest occurrences of a single point is listed, along with an average. These are only guide-posts to help you in selecting a color spread. Through experimentation, one will be able to use these numbers wisely. You will be asked for a desired range. This is the number of points which will fall within a single color. Next you are asked to provide the desired 7 colors to represent the various degrees of “closeness” to the Mandelbrot set. Quite amazing and different results can be achieved with various mixes of colors and range.
To see the results of a new color selection, choose the “Re-draw Screen” option. The re-plotting of the Mandelbrot map is done via machine code, thus cutting a twenty-minute job in half. After the screen has been re-drawn, a mini-menu will appear allowing you to save the new data, return to the main-menu, or simply sit back and enjoy the results. (NOTE: During the re-plotting of the map, the ESC key and any other keys are disabled.)
PUTTING THE PIECES TOGETHER
There are four separate program listings which need to be entered into the computer before your fractal-adventure can begin. Listings 2 – 4 will compose the different machine code routines used by the BASIC listing 1. Carefully key-in listings 2 – 4 and save before running them. Each of these machine code listings will automatically save the code to microdrive #1, so insure that there is a suitable cartridge in that drive before running them. The BASIC listing should be saved on the same cartridge (or disk) as the supporting machine code routines. (NOTE: Save Listing 1 with the name “Mandelbrot”.) The main BASIC listing will automatically load the needed machine code routines when executed. Once you have successfully run and de-bugged all aspects of the program, you may safely delete the BASIC machine code loaders (listings 2 – 4 ONLY).
TOWARDS THE FUTURE
A complete break-down of the BASIC program along with extensive information on the machine code routines (including source code) will be provided in your next issue of Time Designs Magazine.
Further Reading:
1. Mandelbrot, Benoit B. The Fractal Geomety of Nature. New York; W.H. Freeman and Company, 1983.
2. Peitgen, H. -O. and P. H. Richter The Beauty of Fractals; Images of Complex Dynamic Systems. Berlin, New York; Springer-Verlag, 1986.
3. Dewdney, A. K. “Computer Recreations: A Computer Microscope Zooms in for a Look at the Most Complex Object in Mathematics.” Scientific American. August 1985. pages 16-24.
4. Schroeder, Peter B. “Plotting the Mandelbrot Set.” Byte. December 1986. pages 207-210.
5. Nachbaur, Fred “Mandelplot: Mathematical Print Art.” SuncWare News. May-June 1986. pages 11-14.
6. McDermott, Jeanne “Geometrical Forms Known As Fractals Find Sense in Chaos.” Smithsonian, December 1983. pages 110-117.
The author will provide the complete program on micro-cartridge for $7.50 (or $4.00 if the sender provides a blank cartridge). Send check or money order to:
Michael E. Carver
1016 N. E. Tillamook
Portland, OR 97212
LISTING 1
10 REMark ** **
20 REMark ** Mandelbrot BASIC **
30 REMark ** Michael E. Carver **
40 REMark ** **
50 :
60 initial
70 main_prog
80 :
1000 DEFine PROCedure main_prog
1010 REPeat bigloop
1020 main_menu
1030 store_it
1040 done
1050 END REPeat bigloop
1060 END DEFine main_prog
1070 :
1080 DEFine PROCedure back_door
1090 FOR m=mm TO 199
1100 FOR n=nn TO 199
1110 k=CODE(INKEY$)
1120 IF k=27 THEN mini_menu
1130 cr=n*gap+ac: ci=m*gap+bc
1140 CALL (start+14)
1150 CALL (plotter+704)
1160 END FOR n
1170 nn=0
1180 END FOR m
1182 mini_window
1184 PRINT #8;"To Save --""Ready ";dev$" Press any key""To Continue"
1186 a$=INKEY$(-1)
1187 paste
1190 END DEFine back_door
1200 :
1210 DEFine PROCedure done
1220 LOCal key
1230 REPeat done_loop1
1240 snap_shot: mini_window
1250 PRINT #8;"ESC = View""F1 = Main Menu"
1260 REPeat done_loop2
1270 key=keyin1
1280 SELect ON key
1290 ON key=27: EXIT done_loop2
1300 ON key=232: CLOSE #8: EXIT done_loop1
1310 END SELect
1320 END REPeat done_loop2
1330 paste
1340 key=CODE (INKEY$(-1))
1350 END REPeat done_loop1
1360 END DEFine done
1370 :
1380 DEFine PROCedure store_it
1390 REPeat check1
1400 overwrite=0
1410 OPEN_NEW #7,dev$&"dir_copy"
1420 DIR #7,dev$: CLOSE #7
1430 OPEN_IN #7,dev$&"dir_copy"
1440 INPUT #7;na$: INPUT #7,na$
1450 REPeat check2
1460 IF EOF (#7) THEN EXIT check2
1470 INPUT #7;na$
1480 IF LEN(na$)>LEN(name$)
1490 IF na$(1 TO LEN(name$)+1)=name$&"_": check_dev: EXIT check2
1500 END IF
1510 END REPeat check2
1520 CLOSE #7: DELETE dev$&"dir_copy"
1530 IF overwrite=0: EXIT check1
1540 END REPeat check1
1550 BORDER #8,2,0: CLS #8
1560 CLOSE #8: IF keep THEN paste
1570 mm=m: nn=n
1580 SBYTES dev$&name$&"_scr",131072,32768
1590 SBYTES dev$&name$&"_dat",start,40710
1600 OPEN_NEW #7,dev$&name$&"_dat2"
1610 PRINT #7;PEEK_L(start+642)-start
1620 PRINT #7;mm: PRINT #7;nn
1630 PRINT #7;gap: PRINT #7;ac: PRINT #7;bc
1640 FOR xx=0 TO 255: PRINT #7,color(xx)
1650 CLOSE #7
1660 mini_menu
1670 END DEFine store_it
1680 :
1690 DEFine PROCedure check_dev
1700 mini_window
1710 PRINT #8;"Overwrite?""(y or n)"
1720 a$=INKEY$(-1)
1730 IF a$=="y"
1740 DELETE dev$&name$&"_scr"
1750 DELETE dev$&name$&"_dat"
1760 DELETE dev$&name$&"_dat2"
1770 overwrite=0
1780 ELSE
1790 CLOSE #7:DELETE dev$&"dir_copy"
1800 CLS #8: INPUT #8;"New device " dev$
1810 CLS #8: INPUT #8;"New Name " name$
1820 overwrite=1
1830 END IF
1835 paste
1840 END DEFine check_dev
1850 :
1860 DEFine PROCedure mini_window
1870 keep=0
1880 IF m>=164 THEN keep=1: snap_shot
1890 OPEN #8,con_192x36a56x0_32
1900 BORDER #8,2,0,5: CLS #8
1910 END DEFine mini_window
1920 :
1930 DEFine PROCedure main_menu
1940 LOCal a$,b$,x,y
1950 tv: PAPER 4: INK 7: BORDER 4,2,4: CLS: OVER 0
1960 CSIZE 3,0: STRIP 1: CURSOR 134,18: PRINT " "
1970 CURSOR 128,14: STRIP 2: PRINT "MANDELBROT"
1980 CSIZE 2,0
1990 RESTORE 2080
2000 x=32: y=52
2010 FOR i=1 TO 4
2020 a$=FILL$(" ",2): b$=FILL$(" ",23)
2030 STRIP 1: CURSOR x,y: PRINT a$: CURSOR x+72,y: PRINT b$
2040 READ a$,b$
2050 STRIP 2: CURSOR x-6,y-4: PRINT a$: CURSOR x+66,y-4: PRINT b$
2060 y=y+24
2070 END FOR i
2080 DATA "F1"," Define New Parameters ","F2"," Re-Draw Screen "
2090 DATA "F3"," Load Screen and Data ","F4"," Re-Define Color Data "
2100 REPeat response
2110 key=keyin1
2120 SELect ON key=232,236,240,244 : EXIT response
2130 END REPeat response
2140 SELect ON key
2150 ON key=232: set_up
2160 ON key=240
2170 recall
2180 IF back=232 AND m<199 AND n<199
2182 back_door
2185 RETurn
2190 ELSE main_prog
2200 END IF
2210 ON key=244: re_color
2220 ON key=236: redraw
2230 END SELect
2240 SELect ON key
2250 ON key=232
2260 BORDER 6,0: CLS: canvas: CLS #2
2270 back_door
2280 ON key=100: RETurn
2290 ON key=REMAINDER : main_prog
2300 END SELect
2310 END DEFine main_menu
2320 :
2330 DEFine PROCedure mini_menu
2340 LOCal key,key$
2350 mini_window
2360 PRINT #8,"row ";m;" ";"col ";n
2370 PRINT #8, "F1 = Save""F2 = Cont""F3 = Restart"
2380 REPeat query2
2390 key=keyin1
2400 SELect ON key
2410 ON key=232: store_it: mini_window: EXIT query2
2420 ON key=236: EXIT query2
2430 ON key=240
2440 CLS #8: PRINT #8;"Okay to""Abandon?"" (y or n)"
2450 key$=INKEY$(-1): IF key$=="y" THEN main_menu: EXIT query2
2460 EXIT query2
2470 END SELect
2480 END REPeat query2
2490 BORDER #8,2,0: CLS #8
2500 CLOSE #8
2510 IF keep THEN paste
2520 END DEFine mini_menu
2530 :
2540 DEFine PROCedure initial
2550 LOCal x,y,i
2560 tv: PAPER 1: INK 0: BORDER 4,2,1: CLS: CSIZE 3,1
2570 x=64: y=68
2580 FOR i=1 TO 16
2590 CURSOR x,y: OVER 1: PRINT "M A N D E L B R O T"
2600 x=x-1: y=y-(i MOD 2)
2610 END FOR i
2620 CURSOR x,y: INK 2: PRINT "M A N D E L B R O T"
2630 canvas
2640 start=RESPR(40710): LBYTES mdv1_mandelbrot_code,start
2650 camera=RESPR(1808): LBYTES mdv1_snapshot_code,camera
2660 plotter=RESPR(786): LBYTES mdv1_plotter_code,plotter
2670 DIM color(255)
2680 color(0)=4
2690 FOR i=1 TO 58 STEP 2
2700 color(i)=6: color(i+1)=4
2710 END FOR i
2720 color(59)=5: color(60)=5
2730 FOR i=61 TO 66: color(i)=4
2740 FOR i=67 TO 82: color(i)=3
2750 FOR i=83 TO 89: color(i)=2
2760 FOR i=90 TO 102: color(i)=1
2770 FOR i=103 TO 118: color(i)=6
2780 FOR i=119 TO 139: color(i)=5
2790 FOR i=140 TO 162: color(i)=4
2800 FOR i=162 TO 192: color(i)=3
2810 FOR i=193 TO 229: color(i)=2
2820 FOR i=230 TO 254: color(i)=1
2830 FOR i=0 TO 255: POKE (plotter+208+i),color(i)
2840 dev$="mdv2_": name$="mandelbrot"
2850 END DEFine initial
2860 :
2870 DEFine PROCedure set_up
2880 LOCal dev1$,name1$,key
2890 REPeat query
2900 PAPER 2: BORDER 4,2,5: CSIZE 2,0: CLS
2910 AT 2,0
2920 INPUT "Co-ords of proposed Mandelbrot""set""A-Corner [Real Part] ";ac
2930 INPUT "B-Corner [Imaginary Part] ";bc
2940 INPUT "Length of each side ";s
2950 INPUT "Device Name "&dev$dev1$
2960 INPUT "Save as "&"'"&name$&"'"name1$
2970 IF dev1$<>"" THEN dev$=dev1$
2980 IF name1$<>"" THEN name$=name1$
2990 CLS
3000 PRINT"Real Part = ";ac
3010 PRINT"Imaginary Part = ";bc
3020 PRINT"Side = ";s
3030 PRINT"Saving as "&"'"&dev$&name$&"'"
3040 PRINT"Are you satisfied with the above?"
3050 key=keyin1
3060 SELect ON key=89,121: EXIT query
3070 END SELect
3080 END REPeat query
3090 gap=s/200: mm=0: nn=0: calc=0
3100 CALL (start)
3110 array=start+710
3120 POKE_L (plotter+188),array: POKE_W (plotter+192),0: POKE_W (plotter+194),0
3130 END DEFine set_up
3140 :
3150 DEFine PROCedure recall
3160 LOCal dev1$,name1$,key
3170 PAPER 5:INK 0: CLS: AT 2,0
3180 INPUT 'Load from Device ? "'&dev$&'"'dev1$
3190 IF dev1$<>"" THEN dev$=dev1$
3200 CLS: DIR dev$
3210 PRINT: INPUT 'Name ? "'&name$&'"'name1$
3220 IF name1$<>"" THEN name$=name1$
3225 canvas
3230 LBYTES dev$&name$&"_scr",131072
3240 LBYTES dev$&name$&"_dat",start
3250 OPEN_IN #7,dev$&name$&"_dat2"
3260 INPUT #7,a: array=a+start
3270 INPUT #7,mm: INPUT #7,nn
3280 INPUT #7,gap: INPUT #7,ac: INPUT #7,bc
3290 FOR xx=0 TO 255: INPUT #7,color(xx): POKE (plotter+208+xx),color(xx)
3300 CLOSE #7
3310 POKE_L start+642,array: POKE_L plotter+188,array
3320 REPeat recall_loop1
3330 m=mm: n=nn: calc=0
3340 POKE_W (plotter+192),m: POKE_W (plotter+194),n
3350 mini_window
3360 PRINT #8;"ESC = View""F1 = Continue""F2 = Main Menu"
3370 REPeat recall_loop2
3380 key=keyin1
3390 SELect ON key
3400 ON key=27: BORDER #8,2,0: CLS #8: CLOSE #8: EXIT recall_loop2
3410 ON key=232,236: BORDER #8,2,0: CLS #8: CLOSE #8: EXIT recall_loop1
3420 END SELect
3430 END REPeat recall_loop2
3440 IF mm>=164 THEN paste
3450 key$=INKEY$(-1)
3460 END REPeat recall_loop1
3470 back=key
3480 IF mm>=164 THEN paste
3490 END DEFine recall
3500 :
3510 DEFine PROCedure redraw
3520 LOCal array1
3530 array1=start+710
3540 MODE 8: canvas : BORDER 6,0: PAPER 0: CLS #2: CLS #0: CLS
3550 POKE_L (plotter+188),array1
3560 CALL plotter
3570 REPeat redraw_loop1
3580 mini_window
3590 PRINT #8;"ESC = View""F1 = Save""F2 = Main Menu"
3600 REPeat redraw_loop2
3610 key=keyin1
3620 SELect ON key
3630 ON key=27: BORDER #8,2,0: CLS #8: CLOSE #8: EXIT redraw_loop2
3640 ON key=232: key= 100: EXIT redraw_loop1
3650 ON key=236: BORDER #8,2,0: CLS #8: CLOSE #8: EXIT redraw_loop1
3660 END SELect
3670 END REPeat redraw_loop2
3680 paste
3690 key$=INKEY$(-1)
3700 END REPeat redraw_loop1
3710 IF key<>27 THEN paste
3720 END DEFine redraw
3730 :
3740 DEFine PROCedure re_color
3750 LOCal m,m1,cut_off,check,i,array1,average,total,xx,col(6)
3760 PAPER 2: CLS
3770 REPeat do_calc
3780 IF calc
3790 PRINT "Do you wish to re-calculate Data?"
3800 key$=INKEY$(-1): IF key$<>"y"AND key$<>"Y" THEN EXIT do_calc
3810 END IF
3820 CLS: PRINT "Please prepare a cup of tea as I","will be awhile calculating","requested data. . ."
3830 DIM dat(255): calc=1
3840 array1=start+710
3850 FOR m=0 TO 39999
3860 dat(PEEK(array+m))=dat(PEEK(array+m))+1
3870 END FOR m
3880 high1=1: high2=0
3890 FOR m=1 TO 255
3900 IF dat(m)>high1 THEN high1=dat(m)
3910 IF dat(m)<high1 AND dat(m)>high2 THEN high2=dat(m)
3920 END FOR m: EXIT do_calc
3930 END REPeat do_calc
3940 CLS: PRINT "Highest Range = ";high1"Next Highest = ";high2
3950 total=0
3960 FOR m=0 TO 255: total=total+dat(m)
3970 average=total/256
3980 PRINT "Average Range = ";average
3990 INPUT "Input desired Range ";cut_off
4000 CLS: DIM col(6)
4010 color_bar: STRIP 2: OVER 0
4020 INPUT "2 colors for Furthest Points "col(0),col(1)
4030 INPUT "Next 4 colors (In order progress-ing toward Mandelbrot Set): "col(2),col(3),col(4),col(5)
4040 INPUT "Color for Mandelbrot Set ";col(6)
4050 check=0: m=254: xx=1:yy=6
4060 REPeat outer_loop
4070 m1=m
4080 REPeat inner_loop
4090 check=check+dat(m)
4100 IF check>=cut_off THEN EXIT inner_loop
4110 m=m-1: IF m=0 THEN EXIT inner_loop
4120 END REPeat inner_loop
4130 IF m1-m<=2
4140 xx=xx+(xx=0)-(xx=1)
4150 FOR i=m TO m1: color(i)=col(xx)
4160 ELSE
4170 yy=yy-1
4180 IF yy=1 THEN yy=5
4190 FOR i=m TO m1: color(i)=col(yy)
4200 END IF
4210 check=0
4220 m=m-1: IF m=-1 THEN EXIT outer_loop
4230 END REPeat outer_loop
4240 color(255)=col(6)
4250 FOR xx=0 TO 255: POKE (plotter+208+xx),color(xx)
4260 END DEFine re_color
4270 :
4280 DEFine PROCedure color_bar
4290 LOCal x
4300 FOR x=0 TO 7
4310 PRINT " ";x;"=";: STRIP x: OVER 0: PRINT " ";:OVER 1
4320 END FOR x
4330 END DEFine color_bar
4340 :
4350 DEFine FuNction keyin1
4360 LOCal a$,a
4370 REPeat key1_loop
4380 REPeat waitloop: a$=INKEY$: IF a$="" THEN EXIT waitloop
4390 REPeat getkey: a$=INKEY$: IF a$<>"" THEN EXIT getkey
4400 a=CODE(a$)
4410 RETurn a
4420 END REPeat key1_loop
4430 END DEFine keyin1
4440 :
4450 DEFine PROCedure snap_shot
4460 CALL camera
4470 END DEFine snap_shot
4480 :
4490 DEFine PROCedure paste
4500 CALL (camera+40)
4510 END DEFine snap_shot
4520 :
4530 DEFine PROCedure tv
4540 MODE 8: WINDOW 512,256,0,0
4550 PAPER 0: CLS
4560 WINDOW 420,160,46,0
4570 WINDOW #2,420,160,46,0
4580 WINDOW #0,420,32,46,160
4590 PAPER 2: PAPER #2,1: PAPER #0,0
4600 INK 7: INK #2,7: INK #0,7
4610 CLS: CLS #0
4620 END DEFine tv
4630 :
4640 DEFine PROCedure canvas
4650 WINDOW #2,400,200,56,0
4660 SCALE #2,199,0,0: PAPER #2,0
4670 END DEFine canvasLISTING 2
100 REMark ** Loader for mandelbrot
110 :
120 start=RESPR(712)
130 :
140 REMark *** POKEs Code for mandelbrot
150 :
160 RESTORE 1000
170 FOR x=0 TO 642 STEP 2
180 READ a: POKE_W (start+x),a
190 END FOR x
200 :
210 SBYTES mdv1_mandelbrot_code,start,712
220 :
1000 DATA 28672,16890,706,17402,634,8840,20085,28672
1010 DATA 8814,28,-11314,10761,14396,514,8764,611
1020 DATA 29184,9276,611,26880,16878,32,9296,-10802
1030 DATA 16878,24,8784,-11314,13841,-18365,26370,24602
1040 DATA 18938,80,-11031,2,6362,6362,6362,18938
1050 DATA 66,-19820,26408,-19308,26384,16878,32,9296
1060 DATA -10802,20553,-17783,25296,24628,18938,46,16878
1070 DATA 40,9296,-10802,-10775,4,10378,24796,18938
1080 DATA 22,16878,40,9296,-10802,-10775,4,10378
1090 DATA 24776,0,0,0,0,0,0,18938
1100 DATA 488,9850,-14,14555,10459,21579,14555,10459
1110 DATA 30728,16988,23500,-4,29208,12408,282,20112
1120 DATA 8814,88,18938,448,14524,0,18938,460
1130 DATA 15788,0,-26618,11692,2,-26616,15788,0
1140 DATA -26624,11692,2,-26622,32256,12348,14,12408
1150 DATA 284,20112,15798,-26624,-26374,11702,-26622,-26372
1160 DATA 18938,402,15788,0,-26624,11692,2,-26622
1170 DATA 15788,0,-26618,11692,2,-26616,32256,12348
1180 DATA 14,12408,284,20112,15798,-26624,-26374,11702
1190 DATA -26622,-26372,-27908,12,32256,12348,12,12408
1200 DATA 284,20112,18938,322,15772,-26618,11668,-26616
1210 DATA 32256,12348,10,12408,284,20112,18938,322
1220 DATA 14582,-26624,10422,-26622,-27908,12,11593,86
1230 DATA 15804,2050,-26624,11708,16384,0,-26622,18938
1240 DATA 276,15772,-26618,11676,-26616,32256,12348,14
1250 DATA 12408,284,20112,15772,-26618,11668,-26616,32256
1260 DATA 12348,14,12408,284,20112,18938,226,15772
1270 DATA -26618,11668,-26616,32256,12348,10,12408,284
1280 DATA 20112,18938,214,14582,-26624,10486,-26622,19450
1290 DATA 196,15196,0,11100,2,-27908,18,11593
1300 DATA 88,15789,0,-26624,11693,2,-26622,15773
1310 DATA -26618,11677,-26616,32256,12348,14,12408,284
1320 DATA 20112,23625,15789,0,-26624,11693,2,-26622
1330 DATA 15789,0,-26618,11693,2,-26616,32256,12348
1340 DATA 14,12408,284,20112,23881,15798,-26374,-26624
1350 DATA 11702,-26372,-26622,32256,12348,10,12408,284
1360 DATA 20112,32256,12348,4,12408,284,20112,15414
1370 DATA -26624,-27908,22,11593,88,18938,42,14868
1380 DATA 3142,4,27648,14,21061,14469,3077,255
1390 DATA 26112,-422,10362,12,6341,19450,6,10892
1400 DATA 20085,0LISTING 3
100 REMark ** Loader for plotter
110 :
120 plotter=RESPR(786)
130 :
140 REMark *** POKEs plotter code
150 :
160 RESTORE 1000
170 FOR x=0 TO 187 STEP 2
180 READ a: POKE_W (plotter+x),a
190 END FOR x
200 :
210 FOR x=704 TO 784 STEP 2
220 READ a: POKE_W (plotter+x),a
230 END FOR x
240 :
250 SBYTES mdv1_plotter_code,plotter,786
260 :
1000 DATA 18938,190,16980,12820,17914,186,24832,88
1010 DATA 18938,176,16980,17914,164,18426,180,24832
1020 DATA 98,1682,0,1,18938,152,12820,17914
1030 DATA 154,24832,50,17914,140,24832,94,17914
1040 DATA 130,1618,1,3154,199,28618,19450,114
1050 DATA 1621,1,12821,17914,108,24832,10,3157
1060 DATA 199,28588,20085,8814,88,15745,-26624,28680
1070 DATA 32256,12408,284,20112,13558,-26624,9398,-26622
1080 DATA 20085,30208,10322,-10732,-10557,4627,28713,8316
1090 DATA 2,2,30463,20035,20085,17402,532,13146
1100 DATA 0,9050,2,13146,6,9050,8,28720
1110 DATA 30463,8316,2,2,20035,20085
2000 DATA 18938,-514,12820,17914,-516,24832,-614,17914
2010 DATA -532,18426,-516,24832,-598,1682,0,1
2020 DATA 18938,-544,12820,17914,-542,24832,-646,17914
2030 DATA -556,24832,-602,17914,-566,1618,1,3154
2040 DATA 199,28416,12,16978,19450,-586,1621,1
2050 DATA 20085LISTING 4
100 REMark *** Loader for Snapshot code
110 :
120 camera=RESPR(80)
130 :
140 REMark *** POKEs Code for Camera
150 :
160 RESTORE 1000
170 FOR x=0 TO 79 STEP 2
180 READ a: POKE_W (camera+x),a
190 END FOR x
200 :
210 SBYTES mdv1_snapshot_code,camera,80
220 :
1000 DATA 8828,1,-4,16890,72,28672,29185,29697
1010 DATA 12505,20994,3074,24,28662,-11524,80,20993
1020 DATA 3073,36,28648,20085,8828,1,-4,16890
1030 DATA 32,28672,29185,29697,13016,20994,3074,24
1040 DATA 28662,-11524,80,20993,3073,36,28648,20085Note: Type-in program listings on this website use ZMAKEBAS notation for graphics characters.