╘HIS IS AN ARTISTIC SECTION WITH MATHEMATICAL ORIGINS. ╘HE PROGRAM DRAWS AN ENORMOUS VARIETY OF DESIGNS. ╚ERE IS AN ILLUSTRATION OF ONE DESIGN:
// PIXPIC: S2.9.2.11 //
╧RIGINAL PROGRAM ╙╒╨┼╥╧╙┼ WAS PUBLISHED FOR THE ├OMMODORE ╨┼╘ COMPUTER A LONG TIME AGO IN THE ═╔├╥╧ MAGAZINE. ╔ DO NOT HAVE ANY FURTHER INFORMATION ABOUT THE SOURCE. ╫E DO NOT REALLY NEED IT, AS THE PLOTTING COMMANDS ARE STANDARD GEOMETRY NOT OWNED BY ANYBODY.
╘HIS PROGRAM INVITES YOU TO TRY THINGS OUT BY CHANGING LINE 110. ╔N FACT, SOME DETAILS WILL BE OMITTED ON PURPOSE, TO LET YOU PLAY WITH THIS PROGRAM:
// PRG: SUPEROSE//
Ç*FP7
*** ╓┴╥╔┴┬╠┼╙ ***
╠ IF SET TO 0 WE DRAW POINTS
IF SET TO -1 WE DRAW LINES
╦ CORRECTION FOR ╘╓
╙─ PLOT DENSITY - HOW FREQUENT THE POINTS
╘, ╙╪, ╙┘ ARE FOR YOU TO PLAY WITH
╚╪ MIDPOINT ON THE ╪ COORDINATE (HORIZONTAL)
╚┘ MIDPOINT ON THE ┘ COORDINATE (VERTICAL)
FLIPPED, SO THAT POINT 0,0 IS IN THE
LOWER LEFT-HAND CORNER
*** ╔╬╙╘╥╒├╘╔╧╬╙ ***
╥╒╬ IT AND WATCH THE SHOW. ╘HERE IS A FLASHING "╦┼┘" WORD IN THE CORNER TO REMIND YOU THAT TO STOP THE DRAWING YOU CAN PUSH ANY KEY. ╙O LONG AS THE SIGN IS FLASHING, THE COMPUTER PLOTS ITS WAY, SOMETIMES RETRACING OLD PATH.
╙O, PRESS ANY KEY TO EXIT THE DRAWING OR TO EXIT THE GRAPHIC MODE AFTER THE PLOT IS COMPLETE.
┴S SOON AS YOU EXIT THE PROGRAM IT AUTOMATICALLY ╠╔╙╘S LINE 110 FOR YOU. ╘HIS LINE CONTAINS THE IMPORTANT PLOTTING PARAMETERS, SO IT IS ALL READY FOR YOU TO MODIFY.
*** ╨╥╧╩┼├╘╙ ***
═ODIFY THE PARAMETERS, AS SUGGESTED ABOVE.
╘HIS IS A VERY INTERESTING PROGRAM. ╞IRST OF ALL, DID YOU NOTICE THAT ALL PLOTTING IS CONFINED TO THE SCREEN? ╬OTHING JUMPS OUTSIDE. ╔T IS AS IF YOU HAD A PENCIL ATTACHED TO THE MIDDLE OF THE SCREEN WITH A RUBBER BAND. ╔T GOES FAR AWAY AND COMES RIGHT BACK.
╘HAT'S PART OF THE BEAUTY IN SOME MATHEMATICS. ╘HE OTHER NEAT ASPECT OF THE FORMULA USED FOR THE DISPLAYS IS THAT ONE FORMULA CAN DRAW SUCH A VARIETY OF PATTERNS. ╘HE PATTERNS BELONG TO A FAMILY OF CURVES - ONE DEFINITION, BUT DIFFERENT PARAMETERS, WHICH YOU HAVE BEEN CHANGING IN LINE 110.
├AN YOU TELL WHAT DO VARIABLES ╙╪, ╙┘, ╙─ AND ╘ DO? ─ID YOU TRY TO GET A CIRCLE IN THE UPPER OR THE LOWER HALF OF THE SCREEN? ╚OW ABOUT A FIVE-LEAVED FLOWER?
╘HE PLOTTING IS DONE BY CALCULATING IN THE SO CALLED ├ARTESIAN (RECTANGULAR COORDINATES) RELATIVE TO POINT 0,0 IN THE BOTTOM LEFT HAND CORNER OF THE SCREEN. ╘HE CALCULATION IS BASED, HOWEVER ON POLAR COORDINATES (0,0 IN THE CENTER, MEASURING OF ANGLES IN RADIANS). ╔ FIND THIS METHOD EASIER, SINCE THE ADJUSTMENT FOR THE UNPROPORTIONAL SCREEN SEEMS EASIER TO MAKE (VALUE ╦), BUT YOU CAN TRY YOUR OWN APPROACHES. ╥EAD UP ON THE GRAPHIC COMMANDS IN THE MANUAL.
╘HERE ARE MANY FORMULAS IN MATHEMATICAL TEXTS THAT ARE WORTH PLUGGING INTO THE COMPUTER FOR PLOTTING. ╙PIRALS COME TO MIND, THE FORMULA IS SURPRISINGLY SIMPLE. ╘RY TO DESIGN YOUR OWN CODE TO DRAW A SPIRAL FROM INSIDE OUT, THEN OUTISDE IN, THEN WITH VARYING DISTANCES BETWEEN ITS LINES, AND SO ON.
