This route is built from square cells, so it can only travel in eight directions: along the sides and along the diagonals. A real line can run at any angle. To go at 22.5 degrees it has to zigzag between two of the eight, and the zigzag makes it up to 8.2% longer than the straight line it is copying.
The general point is older than this page. A path found on a grid never settles onto the path you would draw on open ground, and how far apart they end up depends on which moves the grid allows. Eight is only one choice.
This route runs close to the diagonal, where the error is smallest. Measured against a true straight line between the same two points, the grid adds 0.5% here. Send the route in another direction and the same method adds more.
For more, see: Goodchild, M. F. 1977. An evaluation of lattice solutions to the problem of corridor location. Environment and Planning A 9(7), 727–738.
The heavy line is the best route these numbers can produce. It is not the only good one. This control draws up to six more routes that the same numbers score almost the same, and shades the land any of them could use. At the tightest setting there are fewer, because fewer of them run far enough apart to be worth drawing separately.
The thin routes are real answers, not sketches. Each one is the best route that goes through some particular place, and each is within the percentage you choose of the heavy line. They are picked to be as far apart as the shading allows, so you see the range rather than six versions of the same line.
How they are found: costs are added up outward from the substation, then outward from the plant. Add the two surfaces and every cell holds the cost of the best route passing through it, which is all you need to draw one.
Set it to 0.1% and one of the thin routes runs over different ground for more than half its way, for a cost a thousandth higher. That is not a near miss. It is a tie, and the software picked between them without telling you.
How arbitrary that pick is, measured on this page: changing the order the program keeps its unfinished work in — a detail with nothing geographic in it at all — moved half of the heavy line onto different ground, at a cost identical to every decimal place we can print. Both answers were right. Only one of them was going to be shown.
Software normally shows the heavy line and nothing else. Read the area printed beside the length to see how much room the alternatives have.
For more, see: Pinto, N. and Keitt, T. H. 2009. Beyond the least-cost path: evaluating corridor redundancy using a graph-theoretic approach. Landscape Ecology 24, 253–266.