String Art

by Professor Virginia Jones

Inspired by the mathematical research of Harlan Brothers at the Country School in Madison, CT, Prof. Virginia Jones at Central Connecticut State University created Terrapin Logo procedures to show Koch string variations.

This project illustrates Koch string variations.

KochStrings.lgo

to koch_hb :length :level :theta
  ; This procedure was created by Harlan Brothers, 2003.
  if (:level = 0) [fd :length stop]
  koch_hb  (:length/(2*(1 + cos (:theta)))) (:level - 1) :theta
  lt :theta
  koch_hb  (:length/(2*(1 + cos (:theta)))) (:level - 1) :theta
  rt 2* :theta
  koch_hb  (:length/(2*(1 + cos (:theta)))) (:level - 1) :theta
  lt :theta
  koch_hb  (:length/(2*(1 + cos (:theta)))) (:level - 1) :theta
end
  
to string
  ; This procedure was created by Virginia Jones, 2003.
  ; This creates a horizontal string "centered"
  ; in the full-screen graphics window with the "tip" of the
  ; string 8 pixels below the home position.
  ; To create a string from a current position of the turtle
  ; use the procedure koch_string by itself
  ; you can change the 198 assigned to :base
  ; which gives half the length of the string base.
  make "base1 198
  cs fs pu rt 90 bk :base1 lt 90 bk :base1 rt 90 pd
  koch_string :base1 * 2
end
  
to koch_string :base2
  ; You can change the variation in the angle theta
  ; by assigning a value other than 88 in the following make command
  ; and subtracting a number other than 4 in the make command
  ; in the repeat line
  ; WARNINGL  You will then need to "adjust" the repeat value of 23 to
  ; an appropriate new number
  make "theta 88
  repeat 23 [ koch_hb :base2 1 :theta make "theta :theta - 4  pu bk :base2 pd]
 end

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Procedure	STRING
Description	Koch string variations
Level	Intermediate
Tags	Koch, Strings, Formulae, Complex Images