The Lo Shu square is a mathematical grid 3 x 3 , where the sum of numbers from each row, column or diagonal is the same- no matter which direction you add the numbers – horizontal, vertical or diagonal – they always add up to 15.
The number 5 is placed in the centre with the even (Yin) numbers at the corners and the odd (yang) ones in-between, forming a cross. This forms the basis of the later heaven bagua which refers to the order of change in the manifest world (as opposed to the "early heaven bagua" archetypal world before creation and change).
The numbers in the Lo Shu Square are considered to have specific properties or be an expression of specific energies. For example, number 9 carries a strong Fire elemental energy, while number 1 is an expression of the water element. In feng shui, they are called "stars" and they have a predicted pattern to their movement. This is used in Flying star feng shui, that enables the movement of the stars throughout time to be charted and therefore the specific energies known. The energies can then be balanced within the home.
Story has it that an ancient Chinese master (650BC) derived the wisdom of the magic square from the patterns on the back of the turtle that he saw coming out to the water. By reading those patterns he saw a deeper pattern of natural rhythms, or laws of the Universe as expressed in the Lo Shu square.