But how was an average citizen to be sure what constituted a weed?
The ordinance doesn't define a weed except to say it's vegetation taller than 10 inches that isn't maintained. Unlike weed ordinances in some places, Chicago's doesn't name specific weeds.
So a few days ago, Cummings filed a legal complaint against the city.
In addition to calling the law downright unconstitutional, and claiming that native plant gardeners like Cummings are being denied their right to freedom of expression, the complaint asserts that the city is raising millions "on the backs of the poor" with a vague law that's hard to interpret and erratically enforced.
"Say we had a law that says it's illegal to speed," said Cummings' attorney, James L. Bowers. "The problem with that law is that it gives each police officer the authority to decide what's a violation of the law. Somebody may think it's 5 miles an hour. Or 10 miles an hour. The problem for the citizen is they don't know what's illegal until the police officer tells them. We're asking the city to write a better law."
Many native plant lovers share Cummings' feeling. Among them is Monica Buckley, an editor for the American Bar Association and self-described "native plants enthusiast."
In her view, not only is the law's height limit confusing, so is the definition of a weed as vegetation that's not maintained.
"That's a very subjective measure," Buckley said. "At this point, we have a city that's ticketing people for vegetable gardens, for shrubs."
The judges are a problem as well.
"There's no knowledge of horticulture among the judges," she said. "If you say, 'These are native plants and I maintain them,' they will not allow argument of any kind."
Native gardens aren't to everyone's taste. No neat rows of tulips. No poodle hedges. They're a riotous collection of plants that shift with the seasons. Some look weedier than others.
Largely on the grounds that aesthetics matter, a court has already rejected one claim that Chicago's weed law is unconstitutional.
Even some native plant lovers might find Cummings' garden a little too unruly. To her, it's just history and nature at work.
"I like the idea of reaching back and bringing in the history of this part of the planet," she said the other day.
She walked the small garden, touching one plant at a time. Bluebells, wild garlic, Solomon's seal.
"This is horsetail. It's prehistoric."
"This little gem right here is pawpaw."
"These are May apples. My idea is to have children walk home from school and be able to pick fruit."
Plants, like the rest of beauty, are in the dreams of the beholder.