I'm not going to bother to read the posts above.
What it comes down to is simple... FLOW is only for stirring the tank water in large tanks, it has nothing to do with filtration effectiveness.
As a general rule of thumb you need one cubic inch of colonized biological media per gallon of tank. Think of it as fish-per-fish. It takes a fish one second to produce as much material as the inch of low density foam reduces to nitrate.
You could go out and buy some cheap children's blocks to get the little inch square by two inch tall single-post blocks then bore a hole through the top to fit in about 7 inches of 3/8 inch diameter pipe and then shove an inch square by inch and half tall chunk of medium density foam up inside. You then use air-hose and a pump to jet air bubbles into the top so they flow up the 3/8ths pipe. This DIY filter will handle a single male Betta day-in-day-out without problem and will maintain its own cycle indefinitely once it is established.
The whole selling point for mass-market filtration is that they can move more water quicker over a small filter to filter larger and larger tanks with the same small HOB system. But honestly filters such as small Tetra and ALL Aqueon systems are useless for biological filtration if left unmodified.
Lets look at what the bacterium need:
Something to grow on
A way to propagate around
Calcium and trace minerals
Temps from 67°F to 83°F
If all those are present then you could cycle a single bio-ball inside a piece of tubing.
What you have to understand is that more than 103% of the rumors about what doesn't work in cycling are spread by the people who don't even understand the basics.
Lets look at a Walstad!
I have some issues with this article... not sure where and who decided that Dr W. endorsed potting soil made mostly of compost which always contains decayed animal and plant matter. Just assume that the correct way to Walstad is to go get a shovel of nice dirt and adjust it with dirt from other locations to get the right soil mixture. Buying a bag of soil is the worst way to start one.
So in the Walstad the plants are the pump and the soil is the mechanical and biological media. Additionally the plants can directly absorb some of the ammonia and nitrite in the water but the predominance of these chemicals is actually slowly pulled down into the soil by the root flow cycle the plants generate. While in the soil these chemicals are consumed by the bacteria and the result is nitrate. A solid rule of thumb for any Walstad arrangement is to never have dirt deeper than the roots of the plants you wish to use. Dirt below that depth is just a harborage for anaerobic and cyanotic bacteria.
The soil bed in a Walstad is the buffering system for the health of the tank... Walstads are not simply NPT. Walstads are tanks ballanced specifically to ONLY need replacement of water, feeding of their population and the replacement of fish that die or become too large for the arrangement. You can have Walstad as small as one liter in size with 1/3 of that volume used in the soil bed.
So a Walstad has about ten cubic inches of filtration per fish due to the speed that the filter cycles. We're talking only a few milliliters per day per inch of fish with the rest of the biological processing relying on diffusion and transpiration.
Opposite of a Walstad is a marine nano-tank. A tank that relies both on filtration capacity AND natural filtration by "live rock" and live coral.
This kind of tank is a little odd to freshwater/tropical enthusiasts because the primary life form in the tank isn't actually a fish or a plant but is a porous material in which the bacteria inhabit the bio-media out in the open in the tank as well as in the rear in some combination of submerged and wet-dry filtration. These tanks are designed for the most hard-core of aquarium fools: "people with way too much money". To set up the cycle in these tanks you have to follow a tight set of parameters for water, heat, light, flow and fish load as well as calculate in how much biological load your coral will add AND remove from the system. These numbers are actually different depending on whether you're going to keep plant eaters, flesh eaters or a combination of both and only the most accomplished aquarium keepers can maintain them year after year without resets and break-downs of the entire tank. Hardness has to be precisely regulated in these tanks and due to the salt water there are almost ZERO planting options, so extraneous solutions such as protein skimmers and phosphate reactors are often needed if you wish to keep the consumption of replacement water to a minimum. The bacteria involved are also slightly different. In a general sense you cannot skimp on biological processing surface area in these tanks. They tend to have 5 or 6 inches of filtration running at high flow rates per inch of fish. A good example is the Fluval Spec nano tank. The filtration system uses a 3"x8"x1.5" foam block with an inserted carbonate nodule bag and the minimum flow on the pump is too high for most freshwater fish to be comfortable. The sea is all about rapid mixing and flow of water. The delicacy of operating these tanks is intense and yet I've seen a two liter fully cycled nano-tank using just a circulation pump and coral/live rock.
In all three of these examples the biological processing occurs in a submerged porous material with water flowing through it. It doesn't occur on the glass or magically based on the water volume of the tank.
For those of you who don't like to side-read. 10 million gallons being serviced by 300,000 gallon per minute filtration. Roughly equivalent to 3gpm in a 100 gallon tank. In order for that to be possible the filtration must be single-pass complete. I can fairly well guarantee that the plants, coral and live rock do a lot of work but if you could imagine keeping a 100g marine tank but only having a whisper i5 filter as a primary filtration backup to your live rock you'll understand that it isn't the size of the tank that matters to the cycle, its the effectiveness of the filter.
You can cycle a Lee's sponge filter in a one liter bottle and keep a fish alive just fine. It isn't the water parameters or the feeding time that are at issue, it is the control over nitrate buildup and the water temperature that make maintaining a small tank difficult.
So when you look at anything written by anybody about how "small tanks can't be cycled" remember that the person is half right but all wrong.
We DON'T cycle tanks, we cycle filters.