Many spaces benefit from symmetry to provide clear structure, sight lines and a sense of balance and proportion. Symmetry is relatively easy to establish provided lines are taken from architecture and other design principles of desire lines, volume and texture are considered.
What makes a space truly stand out and deliver the greatest sense of well being and interest is the inclusion of asymmetry within an otherwise symmetrical layout. Here a large Malus John Downie (crab apple) tree slopes to the left and massed pots planted with pine trees and tulips sit to one side of a symmetrical view to a greenhouse.
This juxtaposition can be seen to strengthen rather than undermine the symmetry beyond.