But if the resistors are constrained to fill the area of the entire painting everything cancels out, reducing to: R = resistivity * (length of painting) / (widt

But if the resistors are constrained to fill the area of the entire painting everything cancels out, reducing to: R = resistivity * (length of painting) / (width of painting * thickness of conducting paint). An example: If you have N parallel resistors constrained to fill the painting, their width (and resistance) must go as 1/N. Plug into the formula you gave and the Ns cancel out, leaving Rt constant.