Blogs

Monte Carlo Sampling of a 3D Shape using Metropolis–Hastings
Monte Carlo Sampling of a …

🎲🐄 Can random sampling recover the shape of a 3D object?

In this experiment I explored a simple idea: instead of rendering a 3D mesh directly, define a probability distribution around the mesh and use Monte Carlo sampling to explore it.

If the probability distribution is designed carefully, the …

Reconstructing the Missing: PDEs, Harmonic Functions, and Building an Inpainting Solver from Scratch
Reconstructing the …

🧮🖼 What should happen inside a missing region of an image?

Not “fill it with AI.”

Not “call a library.”

But mathematically — what should the pixel values be?

I wanted to answer that question from first principles.


The Physics Inspiration

In physics, the Laplace equation

$$ \nabla^2 u = 0 $$ …

When Should You Commit? A Sequential Decision Thought Experiment
When Should You Commit? A …

❤️📊 When should you commit?

I started thinking about commitment not as an emotional decision, but as a sequential decision problem.

Many real-life situations share the same structure: dating, hiring, career moves.
You encounter options one at a time, decisions are irreversible, and you don’t know …