Spirals in BBC Basic

Having seen how to program a circle you are in a good position to produce spirals, in which the radius gradually increases (or decreases) as the "polar angle" winds on beyond 360 degrees.

Our simple circle program is:

Circle

      MODE8:OFF
      ORIGIN 640,512
      R=300
      PLOT69,0,0
      MOVE R,0
      FOR t=0 TO 360
        DRAW R*COSRADt,R*SINRADt
        delay=INKEY(1)
      NEXT

By just making two small modifications we get a nice ....

Archimedes Spiral
Polar Equation: R= a * t
where R is the radius, a is a constant and t is total angle turned

      MODE8:OFF
      ORIGIN 640,512
      MOVE 0,0
      FOR t=0 TO 1440
        REM 4 turns of the screw!
        R=0.3*t
        REM gradually increase the radius
        REM in proportion to the total angle turned
        DRAW R*COSRADt,R*SINRADt
        delay=INKEY(1)
      NEXT

The Logarithmic Spiral
Polar Equation: log R = a * t
where R is the radius, a is a constant and t is total angle turned

      MODE8:OFF
      ORIGIN 640,512
      R=30
      MOVE R,0
      FOR t=1 TO 1440
        REM 4 turns of the screw!
        R=30*(1.002^t)
        REM increase the radius
        REM exponentially with angle
        DRAW R*COSRADt, R*SINRADt
        delay=INKEY(1)
      NEXT

Paste these programs into "BB4W" to see them run. (Help is here)

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