Koch snowflake

[JMR]

I'm trying to write a program to produce a Koch snowflake - is there the equivalent way of rotate left and right by an angle theta and proceed forward as in Turtle? It's been driving me mad trying to do it with PLOT statements, trigonometry and trying to spot a pattern with which I can then loop.
Thanking anyone in anticipation.

[Richard Russell]

I'm trying to write a program to produce a Koch snowflake - is there the equivalent way of rotate left and right by an angle theta and proceed forward as in Turtle? It's been driving me mad trying to do it with PLOT statements, trigonometry and trying to spot a pattern with which I can then loop.
Thanking anyone in anticipation.

Spoiler alert: I've listed below the program I wrote 15 years ago to plot the Koch snowflake, so if you want to challenge yourself to write the code from scratch don't look at it! The approach I took in that program was the standard trigonometrical one of advancing the 'turtle' by distance * COS(angle) in the x-direction and distance * SIN(angle) in the y-direction.


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Code: Select all

      REM The Koch snowflake fractal, Richard Russell, 16-May-2010
      MODE 0
      OFF
      PROCsnowflake(240, 740, 800, 4)
      FILL 640,512
      END

      DEF PROCsnowflake(x, y, size, levels)
      MOVE x, y
      PROCkoch(x, y, size, levels, 0)
      PROCkoch(x, y, size, levels, -2*PI/3)
      PROCkoch(x, y, size, levels, -4*PI/3)
      ENDPROC

      DEF PROCkoch(RETURN x, RETURN y, size, level, angle)
      IF level <= 0 THEN
        x += size*COS(angle)
        y += size*SIN(angle)
        DRAW x, y
      ELSE
        PROCkoch(x, y, size/3, level-1, angle)
        PROCkoch(x, y, size/3, level-1, angle+PI/3)
        PROCkoch(x, y, size/3, level-1, angle-PI/3)
        PROCkoch(x, y, size/3, level-1, angle)
      ENDIF
      ENDPROC

[JMR]

Thank you very much. I'll give it a go myself using your tips.

[Richard Russell]

Thank you very much. I'll give it a go myself using your tips.

Here's the output from my program, greatly slowed down:

output.gif

[JMR]

I had to look and I'm glad that I did because there are things I've never used before such as calling a PROCedure within another one (I hope I've described what I mean clearly) and the term RETURN - showing my ignorance I'm afraid.
I code for fun and I think that this was a bit out of league! I've modified the program to show the first 6 snowflakes from levels = 0 to 6 which looks nice.
Thanks for the program and your help - now I just have to work out how it works!

[Richard Russell]

and the term RETURN - showing my ignorance I'm afraid.

A user-defined function (FN) can only return a single value, so since PROCkoch() updates (i.e. returns) two values - x and y - it's necessary to use the RETURN syntax to achieve that.