This map of Washington D.C. is not of the true nature of the city in 1818, rather an optimized vision of what it could be.
In the bottom left we see the South Fron of the Presidents house. On the right, the East Front of the Capitol of the United States. As noted by the map itself, these are not identical recreations but designs of how the buildings should appear.
While the data produced on this map is from an actual survey, it is still an iconoclastic ideal for the city to strive for. The straight lines, like webbing, are the most iconoic feature and show a pristine optimal view of how the city could be - not the semi-chaotic reality that it would have been.
This ideological view shares in part to the symbolism that Washington D.C. presents. It is the center of American democracy, one that highlights its want for order and structure. It does not take into account the actual nature and slight disorder that goes on.