MauiMapMon

A Python tool for generating chaotic noise images using mathematical chaos maps — including the Logistic, Tent, and Henon maps. Outputs are validated against NIST randomness tests and a cryptographic key is derived from each generated sequence.

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Features

• Three chaos map types: Logistic, Tent, and Henon
• NIST statistical randomness tests (Frequency + Runs)
• PBKDF2-HMAC-SHA256 key derivation from generated sequences
• CLI mode for headless/bash use
• Optional Tkinter GUI (when a display is available)

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Requirements

Install dependencies via pip:

pip install numpy scipy cryptography matplotlib pillow

Note: Tkinter is part of the Python standard library but may need to be installed separately on some systems:

sudo apt install python3-tk   # Debian/Ubuntu
brew install python-tk        # macOS with Homebrew

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Installation

git clone https://github.com/wifiknight45/MauiMapMon.git
cd MauiMapMon
pip install -r requirements.txt

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Usage

CLI Mode (Bash)

Run the script directly. If no display is detected, it automatically launches in CLI mode:

python mauimapmon.py

You will be prompted to enter:

Prompt	Description	Example
x0	Initial condition — a float between 0 and 1	0.5
param	Map parameter (r, mu, or a)	3.9
map_type	One of: logistic, tent, henon	logistic
filename	Output .png filename	output.png

Example session:

$ python mauimapmon.py
Chaotic Image Generator (CLI Mode)
Enter initial condition (x0, e.g., 0.5): 0.5
Enter parameter (r, mu, or a, e.g., 3.9): 3.9
Enter map type (logistic, tent, henon): logistic
Enter output filename (e.g., output.png): my_chaos.png

NIST Frequency Test Passed: True
NIST Runs Test Passed: True
Derived Key: a3f9c21b...
Image saved as my_chaos.png

Force CLI Mode

To skip the GUI even when a display is available, pass any argument:

python mauimapmon.py --cli

GUI Mode

If a display environment is detected and no arguments are passed, the Tkinter GUI launches automatically:

python mauimapmon.py

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Map Parameter Ranges

Each map type has valid parameter bounds. Values outside these ranges will raise an error.

Map Type	Parameter	Valid Range	Chaotic Region
Logistic	r	0 – 4	r ≈ 3.57 to 4
Tent	mu	0 – 2	mu > 1
Hénon	a	0 – 1.4	a ≈ 1.4

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Output

• A 256×256 PNG image filled with values derived from the chaotic sequence
• NIST test results printed to stdout
• A PBKDF2-derived cryptographic key (hex) printed to stdout

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Security Notes

• Each run injects os.urandom entropy into the initial condition, so outputs differ even with the same inputs
• The PBKDF2 key derivation uses 500,000 iterations with a random 16-byte salt
• Output filenames are sanitized — only alphanumeric characters, hyphens, underscores, and dots are accepted (must end in .png)

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License

MIT License — see LICENSE for details.

Chaotic Maps Explained

MauiMapMon uses three chaotic maps to generate sequences. Each map exhibits chaotic behavior, producing unpredictable yet deterministic sequences ideal for randomness applications.

Logistic Map: Definition: Defined by the equation x_{n+1} = r * x_n * (1 - x_n), where x_n is the current state (between 0 and 1) and r is a control parameter. Behavior: For r between 3.57 and 4, the map produces chaotic sequences sensitive to initial conditions (x0). Small changes in x0 or r lead to vastly different outputs. Use Case: Generates pseudo-random sequences for image pixel values due to its simplicity and chaotic properties.

Tent Map: Definition: Defined as x_{n+1} = mu * x_n if x_n < 0.5, else x_{n+1} = mu * (1 - x_n), where x_n is the state (between 0 and 1) and mu is a parameter (typically 0 to 2). Behavior: Resembles a tent shape, producing chaotic sequences for mu close to 2. It’s highly sensitive to initial conditions, similar to the Logistic map. Use Case: Provides an alternative chaotic sequence with uniform distribution properties, suitable for cryptographic applications.

Henon Map: Definition: A two-dimensional map defined by x_{n+1} = 1 - a * x_n^2 + y_n and y_{n+1} = b * x_n, where a and b are parameters (typically a=1.4, b=0.3). Behavior: Produces chaotic sequences in a two-dimensional phase space, creating complex patterns. It’s more computationally intensive but offers richer dynamics. Use Case: Generates intricate sequences for applications requiring higher-dimensional chaos, enhancing randomness in images.