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Rule 30 Cellular Automaton Challenge Part 2 for the Prediction Market Community!

Challenge ends on the end of 12th September.

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Introduction:

Engage with the captivating world of cellular automata through Rule 30, known for its seemingly random patterns derived from simple initial conditions.

The Challenge:

Starting with a single black cell (represented by '1') surrounded by white cells (represented by '0s') as the initial row, apply Rule 30 to determine the pattern's evolution over many iterations.

Starting Row (Seed):

...000000000000000000000100000000000000000000...

(Note: The '1' represents the black cell, and the surrounding '0s' represent white cells. This seed is 41 cells wide with the black cell at the center.)

Rule 30 Definition:

The next state of a cell in Rule 30 is based on its current state and the states of its two neighbors (left and right):

Current Pattern (Left-Center-Right) | Next State

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111 | 0

110 | 0

101 | 0

100 | 1

011 | 1

010 | 1

001 | 1

000 | 0

For the leftmost and rightmost cells, assume a virtual neighbor outside the edge which is always a "0" (white cell).

Your Task:

Determine

the state of the center cell after 103060,123 rows. Count the initial state as row 0.