How Bgrid Works

The Core Concept

BGrid transforms continuous geographic coordinates (Latitude, Longitude) into a discrete, hierarchical address.

Instead of arbitrary numbers, we use the BIP39 wordlist (2048 words) to encode location. This means every “cell” in our grid is identified by a single word.

To address the entire world with precision, we nest these grids.

Level 1: The Global Grid

The world is projected onto a 2D plane ($x, y$ normalized to $[0, 1]$). We divide this plane into 2048 cells.

$$N_{cells} = 64 \times 32 = 2048$$

Why $64 \times 32$? The Earth is twice as wide (360° Longitude) as it is tall (180° Latitude). By using twice as many columns as rows, each cell remains roughly square near the equator.

Level 2: Refinement

Inside each Level 1 cell, we divide again by 2048. However, to maintain aspect ratio and precision, we swap the dimensions:

$$Level 2: 32 \times 64 = 2048$$

This alternating strategy ensures that errors don’t accumulate in one dimension.

The Algorithm

Given a coordinate $(lat, lon)$:

1. Normalize:

   $$x = \frac{lon + 180}{360}, \quad y = \frac{90 - lat}{180}$$

2. Iterate (for each level $L$):

   • Determine dividers:

     • If $L$ is odd: $d_x = 64, d_y = 32$
     • If $L$ is even: $d_x = 32, d_y = 64$

   • Calculate Cell Column and Row:

     $$col = \lfloor x \times d_x \rfloor$$ $$row = \lfloor y \times d_y \rfloor$$

   • Calculate Index (1-2048):

     $$index = (row \times d_x) + col + 1$$

   • Zoom in (update $x, y$ to be relative to current cell):

     $$x = (x \times d_x) - col$$ $$y = (y \times d_y) - row$$

This process repeats until the desired precision is reached.

• Level 4 gives accuracy within meters (comparable to GPS for navigation).

Why BIP39?

The BIP39 standard defines a list of 2048 distinct, memorable words. It was designed for Bitcoin seed phrases, but it’s perfect for coordinates because:

1. Error Correction: Words are chosen to be distinct (first 4 letters are unique).
2. Global Support: Wordlists exist for English, Spanish, French, Chinese, etc.
3. Human Friendly: “Apple” is easier to remember than “10010011”.