� DIAGRAMS OF CHAOS
� by Jim Vernon
� (c) The Micro User
(�1
2�'"  ANY FORMULA y=F(x)"
<��'"This prog. graphs F(x) iterated M%"'"times against changing c for the "'"chosen formula. Ranges of y and of c "'"and the initial value of x can be "'"varied."
F��'"The range of c is divided into D%"'"intervals and y is iterated M% times"'"for each value of c, the first T% "'"values ignored and the rest,if within"'"the chosen range of Y, graphed."
P"� Input constants, ranges etc.
Z �'"Formula - in x and c ",X$
d"�'"Limits of c (=C0,C1)",C0,C1
n!�"Limits of y (=Y0,Y1)",Y0,Y1
x�"Initial x (=IX)",IX
�%�"No. of points on c axis(D%)",D%
�1� "Total No. of iterations per val.c(=M%)",M%
�#�"No. not to be printed(T%)",T%
��"Value of XMAX",XMAX
��"NAME of File",A$
��
��19,7,0,0,0,0:�19,0,7,0,0,0
�5� Draw axes (with 10 divisions), mark ranges etc.
��axis(200,150,200,950)
�5� Q%=1 � 10:�axis(200,150+Q%*80,210,150+Q%*80) :�
��axis(200,150,1000,150)
�5� Q%=1 � 10:�axis(200+Q%*80,150,200+Q%*80,160) :�
�
�2,0);A$

�15,1)"y = ";X$

�1,2);Y1:�1,26);Y0

�iter(3,4)

"&�6,28);C0:�19,28)"c":�30,28);C1

,7�0,30)"M%=";M%;" : T%=";T%;" : D%=";D%;" : IX=";IX

6;� Calculate values of F(x) iterated M% times for each c

@K=C1-C0:P=K/D% :L=Y1-Y0

J� c=C0 � C1 � P

Ty=IX

^� N% = 1 � M%

hy=�formula(y)

r$� First T% values of y not shown

|� N%<=T% � @@@@

�YS=(y-Y0)*800/L+150

�CS=(c-C0)*800/K+200

�$� y not plotted if outside range

�� YS<150 � YS>950 � �txA

�� 69,CS,YS

��

�YMAX=(XMAX-Y0)*800/L+150

� � YMAX<150 � YMAX>950 � �djA

�� 69,CS,YMAX

�4� Same calculations and plot for next value of c

��:�save(A$):�

�:

�� Formula defined
� �formula(x)=�(X$)
:
3� Procedure for drawing lines to make axes etc.
&��axis(L%,M%,O%,P%)
0� L%,M%:� O%,P%
:�
D:
N��iter(A%,B%)
X� A$
b� I=1 � 19
l$A$ = �"y iterated M% times",I,1)
v�A%,B%+I)A$
��:�
�:
���cli($&700)�X%,Y%
�Y%=7:�&FFF7:�
�:
�� �save(Z$)
�+� �<&8000 �cli("SAVE "+Z$+" 3000 8000")
�!� �>&8000 �("ScreenSave "+Z$)
��
�

00000000  0d 00 0a 17 f4 20 44 49  41 47 52 41 4d 53 20 4f  |..... DIAGRAMS O|
00000010  46 20 43 48 41 4f 53 0d  00 14 13 f4 20 62 79 20  |F CHAOS..... by |
00000020  4a 69 6d 20 56 65 72 6e  6f 6e 0d 00 1e 18 f4 20  |Jim Vernon..... |
00000030  28 63 29 20 54 68 65 20  4d 69 63 72 6f 20 55 73  |(c) The Micro Us|
00000040  65 72 0d 00 28 06 eb 31  0d 00 32 1c f1 27 22 20  |er..(..1..2..'" |
00000050  20 41 4e 59 20 46 4f 52  4d 55 4c 41 20 79 3d 46  | ANY FORMULA y=F|
00000060  28 78 29 22 0d 00 3c a5  f1 27 22 54 68 69 73 20  |(x)"..<..'"This |
00000070  70 72 6f 67 2e 20 67 72  61 70 68 73 20 46 28 78  |prog. graphs F(x|
00000080  29 20 69 74 65 72 61 74  65 64 20 4d 25 22 27 22  |) iterated M%"'"|
00000090  74 69 6d 65 73 20 61 67  61 69 6e 73 74 20 63 68  |times against ch|
000000a0  61 6e 67 69 6e 67 20 63  20 66 6f 72 20 74 68 65  |anging c for the|
000000b0  20 22 27 22 63 68 6f 73  65 6e 20 66 6f 72 6d 75  | "'"chosen formu|
000000c0  6c 61 2e 20 52 61 6e 67  65 73 20 6f 66 20 79 20  |la. Ranges of y |
000000d0  61 6e 64 20 6f 66 20 63  20 22 27 22 61 6e 64 20  |and of c "'"and |
000000e0  74 68 65 20 69 6e 69 74  69 61 6c 20 76 61 6c 75  |the initial valu|
000000f0  65 20 6f 66 20 78 20 63  61 6e 20 62 65 20 22 27  |e of x can be "'|
00000100  22 76 61 72 69 65 64 2e  22 0d 00 46 bf f1 27 22  |"varied."..F..'"|
00000110  54 68 65 20 72 61 6e 67  65 20 6f 66 20 63 20 69  |The range of c i|
00000120  73 20 64 69 76 69 64 65  64 20 69 6e 74 6f 20 44  |s divided into D|
00000130  25 22 27 22 69 6e 74 65  72 76 61 6c 73 20 61 6e  |%"'"intervals an|
00000140  64 20 79 20 69 73 20 69  74 65 72 61 74 65 64 20  |d y is iterated |
00000150  4d 25 20 74 69 6d 65 73  22 27 22 66 6f 72 20 65  |M% times"'"for e|
00000160  61 63 68 20 76 61 6c 75  65 20 6f 66 20 63 2c 20  |ach value of c, |
00000170  74 68 65 20 66 69 72 73  74 20 54 25 20 22 27 22  |the first T% "'"|
00000180  76 61 6c 75 65 73 20 69  67 6e 6f 72 65 64 20 61  |values ignored a|
00000190  6e 64 20 74 68 65 20 72  65 73 74 2c 69 66 20 77  |nd the rest,if w|
000001a0  69 74 68 69 6e 22 27 22  74 68 65 20 63 68 6f 73  |ithin"'"the chos|
000001b0  65 6e 20 72 61 6e 67 65  20 6f 66 20 59 2c 20 67  |en range of Y, g|
000001c0  72 61 70 68 65 64 2e 22  0d 00 50 22 f4 20 49 6e  |raphed."..P". In|
000001d0  70 75 74 20 63 6f 6e 73  74 61 6e 74 73 2c 20 72  |put constants, r|
000001e0  61 6e 67 65 73 20 65 74  63 2e 0d 00 5a 20 e8 27  |anges etc...Z .'|
000001f0  22 46 6f 72 6d 75 6c 61  20 2d 20 69 6e 20 78 20  |"Formula - in x |
00000200  61 6e 64 20 63 20 22 2c  58 24 0d 00 64 22 e8 27  |and c ",X$..d".'|
00000210  22 4c 69 6d 69 74 73 20  6f 66 20 63 20 28 3d 43  |"Limits of c (=C|
00000220  30 2c 43 31 29 22 2c 43  30 2c 43 31 0d 00 6e 21  |0,C1)",C0,C1..n!|
00000230  e8 22 4c 69 6d 69 74 73  20 6f 66 20 79 20 28 3d  |."Limits of y (=|
00000240  59 30 2c 59 31 29 22 2c  59 30 2c 59 31 0d 00 78  |Y0,Y1)",Y0,Y1..x|
00000250  19 e8 22 49 6e 69 74 69  61 6c 20 78 20 28 3d 49  |.."Initial x (=I|
00000260  58 29 22 2c 49 58 0d 00  82 25 e8 22 4e 6f 2e 20  |X)",IX...%."No. |
00000270  6f 66 20 70 6f 69 6e 74  73 20 6f 6e 20 63 20 61  |of points on c a|
00000280  78 69 73 28 44 25 29 22  2c 44 25 0d 00 8c 31 e8  |xis(D%)",D%...1.|
00000290  20 22 54 6f 74 61 6c 20  4e 6f 2e 20 6f 66 20 69  | "Total No. of i|
000002a0  74 65 72 61 74 69 6f 6e  73 20 70 65 72 20 76 61  |terations per va|
000002b0  6c 2e 63 28 3d 4d 25 29  22 2c 4d 25 0d 00 96 23  |l.c(=M%)",M%...#|
000002c0  e8 22 4e 6f 2e 20 6e 6f  74 20 74 6f 20 62 65 20  |."No. not to be |
000002d0  70 72 69 6e 74 65 64 28  54 25 29 22 2c 54 25 0d  |printed(T%)",T%.|
000002e0  00 a0 19 e8 22 56 61 6c  75 65 20 6f 66 20 58 4d  |...."Value of XM|
000002f0  41 58 22 2c 58 4d 41 58  0d 00 aa 16 e8 22 4e 41  |AX",XMAX....."NA|
00000300  4d 45 20 6f 66 20 46 69  6c 65 22 2c 41 24 0d 00  |ME of File",A$..|
00000310  b4 05 db 0d 00 be 1f ef  31 39 2c 37 2c 30 2c 30  |........19,7,0,0|
00000320  2c 30 2c 30 3a ef 31 39  2c 30 2c 37 2c 30 2c 30  |,0,0:.19,0,7,0,0|
00000330  2c 30 0d 00 c8 35 f4 20  44 72 61 77 20 61 78 65  |,0...5. Draw axe|
00000340  73 20 28 77 69 74 68 20  31 30 20 64 69 76 69 73  |s (with 10 divis|
00000350  69 6f 6e 73 29 2c 20 6d  61 72 6b 20 72 61 6e 67  |ions), mark rang|
00000360  65 73 20 65 74 63 2e 0d  00 d2 1a f2 61 78 69 73  |es etc......axis|
00000370  28 32 30 30 2c 31 35 30  2c 32 30 30 2c 39 35 30  |(200,150,200,950|
00000380  29 0d 00 dc 35 e3 20 51  25 3d 31 20 b8 20 31 30  |)...5. Q%=1 . 10|
00000390  3a f2 61 78 69 73 28 32  30 30 2c 31 35 30 2b 51  |:.axis(200,150+Q|
000003a0  25 2a 38 30 2c 32 31 30  2c 31 35 30 2b 51 25 2a  |%*80,210,150+Q%*|
000003b0  38 30 29 20 3a ed 0d 00  e6 1b f2 61 78 69 73 28  |80) :......axis(|
000003c0  32 30 30 2c 31 35 30 2c  31 30 30 30 2c 31 35 30  |200,150,1000,150|
000003d0  29 0d 00 f0 35 e3 20 51  25 3d 31 20 b8 20 31 30  |)...5. Q%=1 . 10|
000003e0  3a f2 61 78 69 73 28 32  30 30 2b 51 25 2a 38 30  |:.axis(200+Q%*80|
000003f0  2c 31 35 30 2c 32 30 30  2b 51 25 2a 38 30 2c 31  |,150,200+Q%*80,1|
00000400  36 30 29 20 3a ed 0d 00  fa 0d f1 8a 32 2c 30 29  |60) :.......2,0)|
00000410  3b 41 24 0d 01 04 14 f1  8a 31 35 2c 31 29 22 79  |;A$......15,1)"y|
00000420  20 3d 20 22 3b 58 24 0d  01 0e 18 f1 8a 31 2c 32  | = ";X$......1,2|
00000430  29 3b 59 31 3a f1 8a 31  2c 32 36 29 3b 59 30 0d  |);Y1:..1,26);Y0.|
00000440  01 18 0e f2 69 74 65 72  28 33 2c 34 29 0d 01 22  |....iter(3,4).."|
00000450  26 f1 8a 36 2c 32 38 29  3b 43 30 3a f1 8a 31 39  |&..6,28);C0:..19|
00000460  2c 32 38 29 22 63 22 3a  f1 8a 33 30 2c 32 38 29  |,28)"c":..30,28)|
00000470  3b 43 31 0d 01 2c 37 f1  8a 30 2c 33 30 29 22 4d  |;C1..,7..0,30)"M|
00000480  25 3d 22 3b 4d 25 3b 22  20 3a 20 54 25 3d 22 3b  |%=";M%;" : T%=";|
00000490  54 25 3b 22 20 3a 20 44  25 3d 22 3b 44 25 3b 22  |T%;" : D%=";D%;"|
000004a0  20 3a 20 49 58 3d 22 3b  49 58 0d 01 36 3b f4 20  | : IX=";IX..6;. |
000004b0  43 61 6c 63 75 6c 61 74  65 20 76 61 6c 75 65 73  |Calculate values|
000004c0  20 6f 66 20 46 28 78 29  20 69 74 65 72 61 74 65  | of F(x) iterate|
000004d0  64 20 4d 25 20 74 69 6d  65 73 20 66 6f 72 20 65  |d M% times for e|
000004e0  61 63 68 20 63 0d 01 40  1b 4b 3d 43 31 2d 43 30  |ach c..@.K=C1-C0|
000004f0  3a 50 3d 4b 2f 44 25 20  3a 4c 3d 59 31 2d 59 30  |:P=K/D% :L=Y1-Y0|
00000500  0d 01 4a 13 e3 20 63 3d  43 30 20 b8 20 43 31 20  |..J.. c=C0 . C1 |
00000510  88 20 50 0d 01 54 08 79  3d 49 58 0d 01 5e 11 e3  |. P..T.y=IX..^..|
00000520  20 4e 25 20 3d 20 31 20  b8 20 4d 25 0d 01 68 11  | N% = 1 . M%..h.|
00000530  79 3d a4 66 6f 72 6d 75  6c 61 28 79 29 0d 01 72  |y=.formula(y)..r|
00000540  24 f4 20 46 69 72 73 74  20 54 25 20 76 61 6c 75  |$. First T% valu|
00000550  65 73 20 6f 66 20 79 20  6e 6f 74 20 73 68 6f 77  |es of y not show|
00000560  6e 0d 01 7c 13 e7 20 4e  25 3c 3d 54 25 20 e5 20  |n..|.. N%<=T% . |
00000570  40 40 40 40 0d 01 86 17  59 53 3d 28 79 2d 59 30  |@@@@....YS=(y-Y0|
00000580  29 2a 38 30 30 2f 4c 2b  31 35 30 0d 01 90 17 43  |)*800/L+150....C|
00000590  53 3d 28 63 2d 43 30 29  2a 38 30 30 2f 4b 2b 32  |S=(c-C0)*800/K+2|
000005a0  30 30 0d 01 9a 24 f4 20  79 20 6e 6f 74 20 70 6c  |00...$. y not pl|
000005b0  6f 74 74 65 64 20 69 66  20 6f 75 74 73 69 64 65  |otted if outside|
000005c0  20 72 61 6e 67 65 0d 01  a4 1c e7 20 59 53 3c 31  | range..... YS<1|
000005d0  35 30 20 84 20 59 53 3e  39 35 30 20 e5 20 8d 74  |50 . YS>950 . .t|
000005e0  78 41 0d 01 ae 0e f0 20  36 39 2c 43 53 2c 59 53  |xA..... 69,CS,YS|
000005f0  0d 01 b8 05 ed 0d 01 c2  1c 59 4d 41 58 3d 28 58  |.........YMAX=(X|
00000600  4d 41 58 2d 59 30 29 2a  38 30 30 2f 4c 2b 31 35  |MAX-Y0)*800/L+15|
00000610  30 0d 01 cc 20 e7 20 59  4d 41 58 3c 31 35 30 20  |0... . YMAX<150 |
00000620  84 20 59 4d 41 58 3e 39  35 30 20 e5 20 8d 64 6a  |. YMAX>950 . .dj|
00000630  41 0d 01 d6 10 f0 20 36  39 2c 43 53 2c 59 4d 41  |A..... 69,CS,YMA|
00000640  58 0d 01 e0 34 f4 20 53  61 6d 65 20 63 61 6c 63  |X...4. Same calc|
00000650  75 6c 61 74 69 6f 6e 73  20 61 6e 64 20 70 6c 6f  |ulations and plo|
00000660  74 20 66 6f 72 20 6e 65  78 74 20 76 61 6c 75 65  |t for next value|
00000670  20 6f 66 20 63 0d 01 ea  11 ed 3a f2 73 61 76 65  | of c.....:.save|
00000680  28 41 24 29 3a e0 0d 01  f4 05 3a 0d 01 fe 15 f4  |(A$):.....:.....|
00000690  20 46 6f 72 6d 75 6c 61  20 64 65 66 69 6e 65 64  | Formula defined|
000006a0  0d 02 08 17 dd 20 a4 66  6f 72 6d 75 6c 61 28 78  |..... .formula(x|
000006b0  29 3d a0 28 58 24 29 0d  02 12 05 3a 0d 02 1c 33  |)=.(X$)....:...3|
000006c0  f4 20 50 72 6f 63 65 64  75 72 65 20 66 6f 72 20  |. Procedure for |
000006d0  64 72 61 77 69 6e 67 20  6c 69 6e 65 73 20 74 6f  |drawing lines to|
000006e0  20 6d 61 6b 65 20 61 78  65 73 20 65 74 63 2e 0d  | make axes etc..|
000006f0  02 26 17 dd f2 61 78 69  73 28 4c 25 2c 4d 25 2c  |.&...axis(L%,M%,|
00000700  4f 25 2c 50 25 29 0d 02  30 13 ec 20 4c 25 2c 4d  |O%,P%)..0.. L%,M|
00000710  25 3a df 20 4f 25 2c 50  25 0d 02 3a 05 e1 0d 02  |%:. O%,P%..:....|
00000720  44 05 3a 0d 02 4e 11 dd  f2 69 74 65 72 28 41 25  |D.:..N...iter(A%|
00000730  2c 42 25 29 0d 02 58 08  ea 20 41 24 0d 02 62 0e  |,B%)..X.. A$..b.|
00000740  e3 20 49 3d 31 20 b8 20  31 39 0d 02 6c 24 41 24  |. I=1 . 19..l$A$|
00000750  20 3d 20 c1 22 79 20 69  74 65 72 61 74 65 64 20  | = ."y iterated |
00000760  4d 25 20 74 69 6d 65 73  22 2c 49 2c 31 29 0d 02  |M% times",I,1)..|
00000770  76 10 f1 8a 41 25 2c 42  25 2b 49 29 41 24 0d 02  |v...A%,B%+I)A$..|
00000780  80 07 ed 3a e1 0d 02 8a  05 3a 0d 02 94 16 dd f2  |...:.....:......|
00000790  63 6c 69 28 24 26 37 30  30 29 ea 58 25 2c 59 25  |cli($&700).X%,Y%|
000007a0  0d 02 9e 11 59 25 3d 37  3a d6 26 46 46 46 37 3a  |....Y%=7:.&FFF7:|
000007b0  e1 0d 02 a8 05 3a 0d 02  b2 0f dd 20 f2 73 61 76  |.....:..... .sav|
000007c0  65 28 5a 24 29 0d 02 bc  2b e7 20 90 3c 26 38 30  |e(Z$)...+. .<&80|
000007d0  30 30 20 f2 63 6c 69 28  22 53 41 56 45 20 22 2b  |00 .cli("SAVE "+|
000007e0  5a 24 2b 22 20 33 30 30  30 20 38 30 30 30 22 29  |Z$+" 3000 8000")|
000007f0  0d 02 c6 21 e7 20 90 3e  26 38 30 30 30 20 ff 28  |...!. .>&8000 .(|
00000800  22 53 63 72 65 65 6e 53  61 76 65 20 22 2b 5a 24  |"ScreenSave "+Z$|
00000810  29 0d 02 d0 05 e1 0d ff                           |).......|
00000818