A virus gone viral

In a laboratory housed in kotebe micro-organisms were arranged in a \(n\times n\) grid for studying purpose. By accident one of the laboratory technicians spills an infectious virus on some of the organism.This virus has the ability to infect the organism located immediately (east, west, north and south) of its already infected organism in \(3\) microseconds.

How many microseconds does it take for a virus spilled at the center(i=j) of an \(11\times 11\) grid to infect all the organisms.

Details and Assumptions

-Explicit example, \(0\) means infected and \(1\) means normal. If the virus was spilled on the center of a \(3\times 3\) grid.

\[\begin{pmatrix} 1 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 1 \end{pmatrix}\overset { 3\mu s }{ \longrightarrow } \begin{pmatrix} 1 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 1 \end{pmatrix}\overset { 3\mu s }{ \longrightarrow } \begin{pmatrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{pmatrix}\]

For a total of \(6\) microseconds.

The time between getting infected and infecting others is negligible.

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