String Art

by jonesv@ccsu.edu

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. Email Prof. Jones at jonesv@ccsu.edu for a document explaining the mathematics behind the calculations.

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.
  ; If you would like a word document explaining the math
  ; behind the calculation for :length/(2*(1 + cos (:theta)))
  ; please email Virginia Jones at:  jonesv@ccsu.edu
  ; 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
  ; WARNING 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

---

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