J Page

 

The J Language

 

Publications

 

One-dimensional Automata

The Windows form given in the script file uses Cliff Reiter's treatment of one-dimensional three-cell automata given in his Fractals Visualization and J. Second Edition to view any of the 256 possible models. The parameters are the image size, and the paths to the J logo and to the directory for saving images. Radiobuttons are used to select a first row which contains either a random selection of occupied cells or a single centre occupied cell, and also to select the two colours used to diplay the images. The model number, a non-negative integer initially 0, may be specified arbitrarily or allowed to go through the sequence 0, 1, 2, ..., 255.

J4.06 file: automatn.ijs

 

Digits of Pi

Pi may be calculated to an arbitrary number of digits using the marvellous expression
      <.@o. 10x^n  ,
due to Roger Hui, which gives pi exactly to n decimal places. For example, <.@o. 10x^25 is
     31415926535897932384626433 .
This expression is used in the following verbs to give a "pi tree" to an arbitrary number of levels with the tree shown here being produced by the expression PiTree 10:

         3         
        141        
       59265       
      3589793      
     238462643     
    38327950288    
   4197169399375   
  105820974944592  
 30781640628620899 
8628034825342117067


     pi=: [: ": [: <.@o. 10x"_^]
     PiList=: [: pi [: <: [: *: ]
     PiTriangle=: ([: #~ odd) ,/. PiList
          odd=: 1: + 2: * i.
     PiTree=: ([: - [: i. -@]) |."0 1 PiTriangle


The Web contains many references to pi. See, for example, Pi on the Web.

 

Some interesting J pages

 

Home page: http://www.cs.ualberta.ca/~smillie/