More than just stability, it has to do with roll coupling to rudder movement. A trainer like the Kadet will bank and turn with rudder control only, no ailerons. We have a guy at a local field who likes to fly big high-wing gassers on three channels (again no ailerons). He cranks the rudder, and the plane both yaws and banks. He cranks both rudder and elevator, and the plane does a full roll (more like a barrel roll).

In a pattern plane, you want to reduce and ideally eliminate all roll coupling to rudder. A high wing, or mid-wing with a little dihedral, will have proverse roll coupling. Not desirable. A low wing with insufficient dihedral will have adverse roll coupling, which means right rudder will roll to the left. I started pattern flying a Superkraft Cap 232 Sport, which is a low wing model with the only dihedral being in the taper of the thickness of the wing from root to tip--flat from tip to tip on top, but angled slightly on the bottom. This plane had a terrible adverse roll, which I finally learned to mix out on my computer TX. I would give right rudder, and the plane would roll and dive to the left. Drove me nuts until my instructor told me what was going on.

Another design feature that acts like dihedral is sweepback on the wing leading edge, which acts as positive dihedral. You'll see a lot of pattern designs with mid-wing placement and swept back leading edge. This enables neutral roll coupling to rudder and works like positive dihedral in both upright and inverted attitudes, whereas dihedral in the spar would be positive when upright but negative when inverted.

For anyone who has made endless test flights and modifications to arrive at a legitimate, reasonably neutral pattern ship (which leaves me out), it is a bit amusing to talk about "designing a pattern plane" with little understanding of the many subtle trade-offs and inter-relationships involved. You can design a plane that suits your fancy, fly it, and be very happy with it. But if it's not dynamically neutral, or very nearly so, it doesn't really pass muster as a pattern design.

If you want to fly a plane that looks the way you want it, that's great. Good adventure, good learning exercise, lots more interesting than knocking an ARF together or building someone else's kit. But if you want to score well in competition, buy a Zen or any other proven winner. If you want to appropriate an existing design and modify it to your taste, that's OK too. Happens all the time. Find a plane that points well, copy its airfoil, moments, proportions, everything that can be measured, then customize it for your powerplant, build it light, finish it the way you want, then fly it. Great project!