anytime you chop down a tree in acnl there's a chance of it leaving a special symbol on the stump. there's much smaller chance of it happening when using a regular axe and the chances increase with using a gold axe i think? using a silver axe guarantees a special design being left on the stump each time you chop down a tree. also, patterned stumps can produce mushrooms year round
there are different designs for the different tree types (left is fruit, bell + oak trees and right is cedar)