Blocking / Tiling Matrix Multiplication Visualization

This repo generates a single GIF that contrasts two output-selection strategies for matrix multiplication:

• Top: random output selection (high reuse cost across A rows and B columns).
• Bottom: block tiling (compute an N/4 x N/4 output tile to reuse rows/cols).

Each frame increments K (starting at 0), highlights the chosen output(s), and shows the required input elements as a function of N (e.g., 2N, 3N). After the first slide, a short dot-product animation sweeps across the first output row/column while shading in the output cell.

Setup

python3 -m venv .venv
. .venv/bin/activate
python -m pip install --upgrade pip
python -m pip install pillow

Generate the GIF

python3 generate_gif.py --n 16

The output is written to:

out/N-16/matmul_blocking_vs_random_N16.gif

For N=24:

out/N-24/matmul_blocking_vs_random_N24.gif

Configuration

• --n: matrix size (default: 16, must be divisible by 4)
• --cell: pixel size of each matrix cell (default: 16)
• --seed: random seed for the top-row selection (default: 7)
• --duration: frame duration in ms (default: 800)
• --out: output root directory (default: out)

Font sizes (pixels)

Adjust the FONT_SIZES dict in generate_gif.py:

FONT_SIZES = {
    "body_px": 18,
    "section_px": 24,
    "title_px": 28,
}

Animation timing ramps

The acceleration curve is controlled by DOT_RAMP (dot-product sweep) and MAIN_RAMP (rest of the outputs). You can set start/end acceleration and a starting velocity:

DOT_RAMP = {
    "start_factor": 0.4,
    "end_factor": 0.12,
    "min_start_ms": 200,
    "min_end_ms": 80,
    "velocity_start": 2.5,
    "accel_start": 2.0,
    "accel_end": 8.0,
}

Example:

python3 generate_gif.py --n 32 --cell 12 --duration 100