leonardo

Tags:	links, mathematica, python
Subject:	Links, Wolfram demonstrations
Time:	01:58 am

from baseconvert import baseconvert as bc
to2 = lambda n: bc(n, outbase=2, outdigits=" #")

from primes import primes_list as pri
for p in pri(200): print to2(p).rjust(20)

This is part of the output, you can see very nice patterns:

      # 
      ##
     # #
     ###
    # ##
    ## #
   #   #
   #  ##
   # ###
   ### #
   #####
  #  # #
  # #  #
  # # ##
  # ####
  ## # #
  ### ##
  #### #
 #    ##
 #   ###
 #  #  #
 #  ####
 # #  ##
 # ##  #
 ##    #
 ##  # #
 ##  ###
 ## # ##
 ## ## #
 ###   #
 #######
#     ##
#   #  #
#   # ##
#  # # #
#  # ###

Other patterns can be seen in the binary representation of the Fibonacci numbers:

from comb import fibonacciList as fibs
for f in fibs(100): print to2(f).rjust(70)

This is part of the output:

                 #
                # 
                ##
               # #
              #   
              ## #
             # # #
            #   # 
            ## ###
           # ##  #
          #  #    
          ### #  #
         # ####  #
        #  ##   # 
        #### ## ##
       ##   #### #
      # #    ##   
     #     # # # #
     ## #  ## ## #
    # # # ##    # 
   #   # #  # ####
   ## ########   #
  # ## # #  #     
 #  #  # #   #   #
 ### ## #   ##   #
# ######## #    #

More patterns can be found with this simple rule, adding a number to the inverted base-2 representation of itself:
http://demonstrations.wolfram.com/ReversalAdditionSystems/

from baseconvert import baseconvert as bc
to2 = lambda n: bc(n, outbase=2, outdigits=".#")

n = 16 # 35 59 83 155
for i in xrange(35):
    print to2(n)
    n += int(bc(n, outbase=2)[::-1], 2)

This the output (if you print more lines you can see more interesting patterns, they become very cyclic later, for n = 16):

#....
#...#
#...#.
##..##
##..##.
#..##..#
#..##..#.
###..#.##
##.###..#.
#..#.#.##.#
#.#..#.#.##.
#....#####.##
#.##..##.###..
###.###.#.#..#
##....#..#.....
##...##.##...##
##...##.##...##.
#..#.#.#...#.#..#
#..#.#..#.##.#..#.
##.############.##
##.############.##.
#.#..###########...#
#..##.#########.#.##.
#.....#########.#.####
#.####..#######.###....
##..#.########.#.#.##.#
##......#.#####.#.......
##....#...###.###.....##
##....#.....#.#####...##.
#..#..#.#####.#.......#..#
#..#...##...#...###.#.#..#.
##.###...##.#.##...##.##.##
##.##.####....#.####...#.##.
#.#...#..#.##.###..#.####...#
#..##...##.#.#.#..##.#..##.##.

From such things you can see how much close are the usual cellular automata to the normal integer operations like the sum following a bit inversion...

comments: Leave a comment

Tags:	mathematica, python
Subject:	Pythonika V.1.0, a Mathematica - Python bridge
Time:	03:25 pm

Pythonika is a very nice add-on for people that appreciate both Python and Mathematica:
http://dkbza.org/pythonika.html
It works with Python 2.4, 2.5, OSX, Win and Linux, and rather old Mathematica versions too (all binaries included too).

You can activate it inside a Mathematica notebook with just (you must have Python installed too):

Install["C:\\somepath\\Pythonika.exe"];

Then you can use Python in a very simple way, few examples:

Execute Python commands:

Py["a= 52.5+4J"]

Passing Mathematica values to Python:

ToPy["my_generic", 15+2I]

Multiline Python code:

Py["\<
square_roots = list()
for i in range(10):
    square_roots.append(i**.5)
    print square_roots[-1]
\>"]

Defining Mathematica functions in Python:

funcOne = PyFunction["def sqrt(nl): return [n**2 for n in nl]"];

Mathematica is very powerful, but I think its syntax is too much complex and bad to program. With Pythonika I can write Python scripts, and then use the wonderful plotting capabilities of Mathematica in a very quick way. A tiny example:

Install["C:\\somepath\\Pythonika.exe"];
Py["\<
from collections import defaultdict
from string import lowercase
txt = file(\"C:\\somepath\\sometext.txt\").read()
freqs = defaultdict(int)
for c in txt:
    freqs[c] += 1
freqs2 = [freqs.get(c, 0) for c in lowercase]
\>"]

ListPlot[ Py["freqs2"] ]

Output:

comments: Leave a comment

January 12th, 2008

November 17th, 2006