Swapping the endpoint signals flips the sign of the gradient, so the same magnitudes point the gradient in the opposite direction. With left signal 18 and right signal 6 the difference is -12 over 6 m, giving gradient -2 per meter exactly for the stated toy signal ledger; real chemotaxis has noisy gradients, flow perturbations, cell variability, and measurement uncertainty.
Swapping endpoint signals reverses the gradient arrow. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
Reverse the endpoint signals
Now the left signal is 18 and the right signal is 6.
6−18=−12
The sign chooses the gradient direction
Difference -12 over 6 m gives gradient -2 per meter.