A Hot Brick

A brick in the shape of a cube sits on a heated surface capable of heating the bottom of the brick to a constant temperature of 90 degrees. The air around the brick is a constant 25 degrees. A perpendicular section through the center of the brick is a 10x10 array showing the temperature at each of 100 points.

Let's specify that we can determine the temperature change of any point in the array by averaging its temperature with the temperatures of its 8 contiguous points (vertically, horizontally and diagonally). If the point is on the edge or the corner of the array then some of those 8 points will be at the ambient 25 degrees.

Given that at time t=0, the bottom of the brick is at 90 degrees and the rest of the brick is at the ambient 25 degrees, devise a function that will calculate the array of temperatures at a later time t in minutes. You will recalculate the temperatures at one minute intervals. Round them to the nearest degree.

Examples

hot_brick(0) ➞ [
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [90, 90, 90, 90, 90, 90, 90, 90, 90, 90]
]

hot_brick(1) ➞ [
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [39, 47, 47, 47, 47, 47, 47, 47, 47, 39]
  [90, 90, 90, 90, 90, 90, 90, 90, 90, 90]
]

hot_brick(10) ➞ [
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 25, 25, 25, 25, 25, 25, 25, 25, 25]
  [25, 26, 26, 26, 26, 26, 26, 26, 26, 25]
  [26, 27, 28, 28, 28, 28, 28, 28, 27, 26]
  [28, 30, 32, 33, 33, 33, 33, 32, 30, 28]
  [31, 36, 39, 41, 41, 41, 41, 39, 36, 31]
  [38, 47, 51, 53, 54, 54, 53, 51, 47, 38]
  [50, 65, 69, 70, 71, 71, 70, 69, 65, 50]
  [90, 90, 90, 90, 90, 90, 90, 90, 90, 90]
]

Notes

• Due to the symmetry of the problem, the array is always horizontally symmetrical.
• Calculations at any time t are solely based on the previous time's t-1 numbers.