A Random Grid of Squares

Grid Redistricting

pdp1035ct18 - 24x30 inches - collage and acrylic on canvas - Cecil Touchon

A Random Grid of Squares - Grid Redistricting

The nitty gritty of how to end gerrymandering and end up with fair voting.

What the rules require

• Equal population. For U.S. House districts, the deviation must be essentially zero. For state legislatures, total deviation within 10 percent is usually safe.

• Contiguity. Every district must be one piece.

• Voting Rights Act (VRA). Where minority communities are large and compact enough, maps must not dilute their opportunity to elect.

• Practical geography. Districts usually must be built out of census blocks or precincts.

A square-friendly method that works

Think in terms of an adaptive quadtree on an equal-area map of each state.

1. Use an equal-area projection for the state
   For example, Albers Equal Area tailored to that state. This keeps area and therefore population density meaningful when you draw “squares.”

2. Build a population-aware quadtree
   Start with the whole state as one square in projected coordinates. Recursively split any square into four equal squares whenever its estimated population exceeds the target district size. Keep splitting until each leaf square holds roughly the target population. This produces small squares in cities and large squares in rural areas, exactly what you described.

3. Snap to real census geography
   Replace the quadtree’s ideal square edges with the nearest set of census blocks or precincts so you have real, administrable boundaries. Use a solver that moves minimal population across each edge so you remain at near-zero deviation.

4. Enforce contiguity and state borders
   Discard or clip squares that extend outside the state boundary, and ensure the snapped block set remains contiguous.

5. Make it VRA-compliant
   Before finalizing, compute where Section 2 requires minority opportunity districts. Where the quadtree would fracture such a community, merge or slightly reshape neighboring squares to preserve a lawful opportunity district. This can be written as a constraint the solver must satisfy.

6. Introduce randomness the right way
   If you want “no partisan intent,” set your randomness only in the origin and orientation of the quadtree grid and seed of the solver. Publish the seed. Anyone can rerun the process and get the same map, which keeps it auditable.

7. Compactness and aesthetics
   Quadtrees produce boxy, compact shapes by default. Where coastline or rivers force jaggedness, apply a tiny smoothing step that never crosses the population or VRA constraints.

Why this beats a rigid uniform grid

• Pure uniform squares cannot hold equal populations without massive cutting and pasting that shreds communities and triggers VRA problems.

• An adaptive grid changes square size with density, so each district is already close to the right population and remains compact.

Edge cases and fixes

• State edges and odd numbers of districts. The outer ring of squares will be irregular once clipped to the state boundary. Allow slight rectangularity or L-merges on the edges to keep contiguity while hitting the population target.

• Water contiguity. Define contiguity across bridges only if state law permits it, and keep an internal rule set for islands.

• Tiny precincts that “spike” into a district. During snapping, penalize tentacles. This keeps districts clean without changing who is included.

Legal and policy framing

You can write a statute or constitutional amendment that requires:

• An equal-area projection fixed in the text.

• The adaptive quadtree procedure and allowable deviation.

• Public seed disclosure and open-source code.

• A VRA compliance step scored by standard metrics.

• A simple tie-breaker: if multiple solutions satisfy all constraints, pick the one with the smallest sum of perimeters.

Implementation sketch

• Data: Census block populations and precinct shapefiles.

• Algorithms: Weighted quadtree construction, integer programming or network-flow balancing to snap to blocks, and a contiguity check.

• Auditing: Publish the code, the seed, and all intermediate grids. Provide a one-click “rerun with this seed” so the public can verify.

What you gain

• Equal population by design.

• No consideration of parties or incumbents.

• Simple, teachable rules the public can understand.

• Repeatable and auditable outcomes.

What you trade off

• Counties and “communities of interest” will sometimes be split, although far less than a uniform grid.

• In some states, VRA constraints will require visible departures from perfect squares, which is the right call to preserve fair opportunity to elect.

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“Upon the Citizen Rests the Fate of the Nation”

Myself, I am a studio artist and a citizen. My job and my duty is to start the conversation and seed the imagination. It is up to others in the right places to nurture it into a reality. We all have a part to play. What’s your part? Do it.

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Hashtags to use: #CreativeFreedomAct #CultureShiftAct #CreativeSocietyAct

web address: https://www.touchonian.com/s/creative-freedom-act