HaKotel HaMa'aravi

Chaos: Fractal Basin Boundaries

Chaos always makes nice background images for your desktop systems. This is my current image:

Basin boundaries arise in dissipative dynamical systems when two, or more, attractors are present. In such situations each attractor has a basin of initial conditions which lead asymptotically to that attractor. The basin boundaries are the sets which separate different basins. It is very common for basin boundaries to contain unstable chaotic sets. In such cases the basin boundaries can have very complicated fractal structure. Because of this complicated very fine-scaled structure, fractal basin boundaries can pose an impediment to predicting long-term behavior. In particular, if an initial condition is specified with only finite precision, it may be very difficult a priori to determine in which basin it lies if the boundaries are fractal.

Google Code Searching For Coding Bugs.

This is just one simple search for common terms that might be linked to secuirty flaws.

Matrix Fun

A simple program written in python that does matrix addition, 
multiplication, scalar multiplication,
transpose and put the matrix into reduced echelon form. 
The main driver program is matrix_fun.py
which does the matrix operations. The run_gen.sh is a 
bash script that runs the program gen_random_test_file.py. 
gen_random_test_file.py generates a flat text file based on the command line parameters given to it.  

python gen_random_test_file.py - h
USAGE : gen_random_test_file.py[options]
Simple program to generate a test file with
random variables for size, min, max and scalar

options : -sm M, --sizemin = M Rows of matrix (random selection of 1 <>-sM N, --sizemax = N Cols of matrix (random selection of 1 <>-m X, --min = N Minimum value of a random element in the matcies
-M Y, --max = Y Maximum value of a random element in the matcies
-cm C, --scalarmin = C Minimum value for a scalar
-cM B, --scalarmax Maximum value for a scalar
-l L, --length = L Length of the list to generate
-f FILENAME, --filename = FILENAME Filename to write list too.

Then the script runs the matrix_fun.py program against it and outputs the results to a text file. Just check the code out its very simple to follow with no real thought about who the user is. Here is an example of just running matrix_fun.py by its self:

what are the dimensions of matrix A [mxn]:
3x3

Please enter in matrix A one row at a time separated by spaces.
1 2 3
5 6 7
4 5 6

What is the dimensions of your matrix B [mxn]:
3x3

Please enter in matrix B one row at a time separated by spaces.
5 6 3
7 5 2
7 9 2

MATRIX A:
| 1 2 3 |
| 5 6 7 |
| 4 5 6 |

MATRIX B:
| 5 6 3 |
| 7 5 2 |
| 7 9 2 |


If Matrix A and B are both mxn we can add them.

We can add Matrix A and B
A + B =
| 6 8 6 |
| 12 11 9 |
| 11 14 8 |

Please enter a scalar value to multiply matrix A by, (cA)
5
| 5 10 15 |
| 25 30 35 |
| 20 25 30 |

Finding the transpose of A:
| 1 5 4 |
| 2 6 5 |
| 3 7 6 |

Matrix Multiplication (AB)
| 40 43 13 |
| 116 123 41 |
| 97 103 34 |

Putting Matrix A into Reduced echelon form.
Before rref:
| 1 2 3 |
| 5 6 7 |
| 4 5 6 |
Row 0 times -5 added to row 1
| 1 2 3 |
| 0 -4 -8 |
| 4 5 6 |
Row 0 times -4 added to row 2
| 1 2 3 |
| 0 -4 -8 |
| 0 -3 -6 |
Row 1 divided by -4
| 1 2 3 |
| 0 1 2 |
| 0 -3 -6 |
Row 1 times -2 added to row 0
| 1 0 -1 |
| 0 1 2 |
| 0 -3 -6 |
Row 1 times 3 added to row 2
| 1 0 -1 |
| 0 1 2 |
| 0 0 0 |

Would you like to enter another matrix [y/n]