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Political redistricting is the redrawing of electoral district boundaries. It is normally undertaken to reflect population changes. The process can be abused, in what is called gerrymandering, to favor one party or interest group over another, resulting thereby in broadly undemocratic outcomes that misrepresent the views of the voters. Gerrymandering is especially vexing in the United States. This paper introduces an algorithm, with an implementation, for creating districting plans (whether for political redistricting or for other districting applications). The algorithm, Seed-Fill-Shift-Repair (SFSR), is demonstrated for Congressional redistricting in American states. SFSR is able to create thousands of valid redistricting plans, which may then be used as points of departure for public deliberation regarding how best to redistrict a given polity. The main objectives of this paper are: (i) to present SFSR in a broadly accessible form, including code that implements it and test data, so that it may be used for both civic deliberations by the public and for research purposes. (ii) to make the case for what SFSR essays to do, which is to approach redistricting, and districting generally, from a constraint satisfaction perspective and from the perspective of producing a plurality of feasible solutions that may then serve in subsequent deliberations. To further these goals, we make the code publicly available. The paper presents, for illustration purposes, a corpus of 11,206 valid redistricting plans for the Commonwealth of Pennsylvania (produced by SFSR), using the 2017 American Community Survey, along with descriptive statistics. Also, the paper presents 1,000 plans for each of the states of Arizona, Michigan, North Carolina, Pennsylvania, and Wisconsin, using the 2018 American Community Survey, along with descriptive statistics on these plans and the computations involved in their creation. [ABSTRACT FROM AUTHOR]