The program below runs a multiplicity of paths.
Depending upon the initial choice of x and y, the constraint is set by the value of 4*x + mod(y,4); mod(y,4) is to be interpreted as 0, 1, 2 or 3.
This formula generates four sequences which have their own unique pattern.
"4 * x + 1" generates a closed spiral of four lobes which never pass through the centre of the spiral array.
"4 * x + 2" generates a closed two lobed spiral that never passes through the centre.
"4 * x + 3" generates a four lobed spiral which does pass through the centre of the array, AND does trace over paths "already trod."
Lastly "4 * x" creates a never ending diagonal chain.
I wrote the program some 12/15 years ago in response to a "hands-on" maths lesson when it became apparent that the children could never get enough space in playground, where we first walked our paths. Inside we replayed on graph paper (suitably sized). The computer program offered them their verification. {This was done with 9-10 yo's - I can probably find the source - literary documentation - of this if required but do not have it personally}.
Charlie's code in his comment at that location runs in a text environment; the characters locate the ends of lineal segments of the path. That which follows calls up a graphics environment. As such, without having a visual of the pathway I don't think Charlie would arrive as fully as that tabulated above.
Nikki's first comment and her next in relation to 'condition' are also worth attention.
' This program will draw 4 different families of "spirals"
DEFINT A-Z
DECLARE SUB intro ()
DECLARE SUB order ()
DECLARE SUB plot ()
DECLARE SUB centre (Row, Text$)
DECLARE SUB keyproc ()
DECLARE SUB keyin ()
DECLARE SUB startpos ()
DIM SHARED fast
DIM SHARED x
DIM SHARED y
DIM SHARED tm
DIM SHARED z
DIM SHARED l
DIM SHARED s
DIM SHARED v
DIM SHARED gr
DIM SHARED k$
DIM SHARED Rw
DIM SHARED Cl
DIM SHARED or$
DIM SHARED MaxCol
DIM SHARED ScrHeight
DIM SHARED mode
DIM SHARED ScrWidth
SCREEN 9
WIDTH 80, 25
MaxCol = 80
COLOR 15, 8
intro
END
'To create text that is centred
SUB centre (Row, Text$)
Col = MaxCol \ 2
LOCATE Row, Col - (LEN(Text$) / 2 + .5)
PRINT Text$;
END SUB
SUB intro
morespir:
CLS
SCREEN 9, 0, 1, 1
LINE (0, 0)-(639, 349), 5, B
COLOR 7
centre 4, "S P I R A L S"
COLOR 14
centre 7, "This program draws spiral paths."
centre 8, "Each family has its own starting point."
centre 10, "At any time the program may be interrupted"
centre 11, "by pressing the space bar."
COLOR 4
centre 13, "A Reminder message is printed "
centre 14, "in the top right corner of the screen"
COLOR 6
centre 16, "Press any key to go on"
keyin
' Page 2 of intro
CLS
COLOR 9
centre 6, "Enter your spiral order, 1 to 20"
LOCATE 7, 45: PRINT "_ "
Rw = 7: Cl = 45
keyproc
startpos
plot
GOTO morespir
END SUB
' Get a character from the keyboard
SUB keyin
k$ = ""
DO
k$ = INKEY$
LOOP WHILE k$ = ""
END SUB
SUB keyproc
or$ = ""
nextkey:
keyin
IF k$ = "*" THEN SYSTEM
IF or$ = "" AND k$ = CHR$(13) THEN k$ = "": GOTO nextkey
IF k$ = CHR$(13) GOTO leave
IF or$ = "" AND k$ = CHR$(8) THEN k$ = "": GOTO nextkey
IF k$ = CHR$(8) THEN or$ = LEFT$(or$, LEN(or$) - 1): GOTO over
or$ = or$ + k$
over:
LOCATE Rw, Cl: PRINT or$; "_ "
GOTO nextkey
leave:
END SUB
'plots the spiral of the chosen family group
SUB plot
CLS
PRINT gr
tm = 1
FOR f = 1 TO l
FOR s = 1 TO v
COLOR 14: LOCATE 1, 40: PRINT "Press ENTER for next step"
COLOR 8: LOCATE 2, 40: PRINT "Press C to finish spiral"
ON tm GOSUB up, left, down, right
tm = tm + 1
IF tm = 5 THEN tm = 1
NEXT s
NEXT f
GOTO donespir
END
up:
FOR a = 1 TO s
LINE (x, y)-(x, y - z), 7
y = y - z
GOSUB star
NEXT
RETURN
END
left:
FOR a = 1 TO s
LINE (x, y)-(x - z, y), 7
x = x - z
GOSUB star
NEXT
RETURN
END
down:
FOR a = 1 TO s
LINE (x, y)-(x, y + z), 7
y = y + z
GOSUB star
NEXT
RETURN
END
right:
FOR a = 1 TO s
LINE (x, y)-(x + z, y), 7
x = x + z
GOSUB star
NEXT
RETURN
END
star:
LINE (x - 1, y + 1)-(x + 1, y - 1), 14
LINE (x - 1, y - 1)-(x + 1, y + 1), 14
reloc:
IF fast = 1 THEN GOTO quick
keyin
IF k$ = "c" THEN fast = 1
IF k$ = CHR$(32) THEN END
IF k$ <> CHR$(13) THEN GOTO reloc
quick: RETURN
END
donespir:
COLOR 14
LOCATE 23, 48: PRINT "Press any key to go on (or x to end)"
keyin
END SUB
SUB startpos
fast = 0
v = VAL(or$)
z = 24
z = INT(6 * z / v)
x = 320
y = 200
IF v = 1 THEN gr = 1: GOTO jump
gr = (v / 4 - INT(v / 4)) * 4
jump:
l = 4
IF gr = 1 THEN y = 240: x = 350
IF gr = 2 THEN l = 2
IF gr = 3 THEN x = 300: y = 150
IF gr = 0 THEN y = 60: x = 100
END SUB
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