A magical turtle emerged from the water with the curious and decidedly unnatural (for a turtle shell) Lo Shu pattern on its shell: circular dots giving unary (base 1) representations of the integers one through nine are arranged in a 3 X 3 grid.
Early records are ambiguous, referring to a “river map”, and date to 650 BCE, but clearly refer to a magic square by 80 CE, and explicitly give one since 570 CE.
The odd and even numbers alternate in the periphery of the Lo Shu pattern; the 4 even numbers are at the four corners, and the 5 odd numbers (outnumbering the even numbers by one) form a cross in the center of the square. The sums in each of the 3 rows, in each of the 3 columns, and in both diagonals, are all 15 (the number of days in each of the 24 cycles of the Chinese solar year). Since 5 is in the center cell, the sum of any two other cells that are directly through the 5 from each other is 10 (e.g., opposite corners add up to 10, the number of the Ho Tu (河圖)).
The Lo Shu is sometimes connected numerologically with the Ba Gua 八卦 “8 trigrams”, which can be arranged in the 8 outer cells, reminiscent of circular trigram diagrams. Because north is placed at the bottom of maps in China, the 3×3 magic square having number 1 at the bottom and 9 at the top is used in preference to the other rotations/reflections. As seen in the “Later Heaven” arrangement, 1 and 9 correspond with ☵ Kǎn 水 “Water” and ☲ Lí 火 “Fire” respectively. In the “Early Heaven” arrangement, they would correspond with ☷ Kūn 地 “Earth” and ☰ Qián 天 “Heaven” respectively. Like the Ho Tu (河圖), the Lo Shu square, in conjunction with the 8 trigrams, is sometimes used as a mandalic representation important in Feng Shui (風水) geomancy.