Lua College Assignment

This project contains three small Lua programs that connect math concepts to practical programming.

1) Visual Math and Fractals: Simplified Mandelbrot Set

• File: mandelbrot.lua
• What it does: prints an ASCII visualization of a simplified Mandelbrot set in the terminal.
• Core idea: each character position is mapped to a complex number, and iterative divergence determines the symbol intensity.

Run:

lua mandelbrot.lua

2) Algebra and Matrices: Matrix Addition

• File: matrix_sum.lua
• What it does: adds two 3x3 matrices and prints the original matrices and the result.
• Core idea: element-wise addition using nested loops and table indexing.

Run:

lua matrix_sum.lua

3) Fibonacci Sequence

• File: fibonacci.lua
• What it does: computes Fibonacci in two ways (recursive and iterative), then compares call count and execution time.
• Core idea: recursion demonstrates exponential growth in repeated work, while iteration demonstrates a more efficient linear approach.

Run:

lua fibonacci.lua
lua fibonacci.lua 40

Learning Outcomes

• Understand how iterative formulas create fractal structures.
• Apply matrix addition from linear algebra in code.
• Compare recursive and iterative algorithm behavior in Fibonacci.
• Observe how implementation choice impacts performance.