Are the patterns on Christmas stockings related to elements of Christmas? 

The patterns on Christmas stockings are usually associated with elements of Christmas. These patterns include, but are not limited to:
Santa Claus: Santa Claus is one of the symbols of Christmas. He is usually depicted as a kind old man wearing a red suit, carrying gifts and a sack. His image often appears in the design of Christmas stockings, symbolizing the delivery of gifts.
Christmas Tree: The Christmas tree is another important element of Christmas, used to decorate and adorn festive places. On Christmas stockings, you can see patterns of Christmas trees, sometimes even with decorations and gifts hanging on them.
Snowflakes: Snowflakes are one of the common patterns of winter and Christmas, representing the cold season and the atmosphere of the holiday. Designs on Christmas stockings may include patterns of snowflakes to enhance the festive atmosphere.
Reindeer: Santa Claus's reindeer are usually depicted as his mode of transportation. They also often appear in the design of Christmas stockings, complementing Santa Claus.
Bells and Gifts: Bells are one of the common decorations of Christmas, representing the joy and happiness of the holiday. Gifts are a traditional symbol of Christmas and are usually depicted on Christmas stockings, implying the gifts brought by Santa Claus.
These patterns are closely related to the themes and atmosphere of Christmas, adding color and interest to Christmas stockings.