In a winter day, I noticed the water frozen inside a canal in our building. As you see there are very nice geometric patterns formed by the ice, with specific angles. What is the physical interpretation of these patterns? Are the giant cristals? The only physical inputs that I can think of is the shape of the canal: width ~30cm and depth of water ~10cm
They are crystals of ice which grow outward from nucleation sites, where the freezing process prefers to start. Those crystals expand until they hit an edge of the container, or another crystal as it grows.
This effect is exploited in a process called directional casting, in which a gas turbine blade can be grown as a single crystal from molten superalloy by cleverly initiating the freezing process at one end of the blade so only the crystallite with the desired lattice orientation can take over and grow. The resulting blade has exceptional strength because it has no grain boundaries, and the lattice orientation provides maximum strength.