Okay, but may I offer an illustration that characterizes the idea of "atonement"?
Debbie and Sam are playing in the house. Father already commanded the children to never to run in the house. But as play increased, Debbie tripped and upset an expensive vase. The vase was ruined and Debbie felt very sorry, especially as Father expressed his anger very sternly.
After an hour or so, Debbie went outside and picked some lovely flowers, brought them into the house, put them into a glass of water and said, "Here Dad. I'm so sorry I broke the vase." Dad was touched so deeply and his feelings for his daughter were so warm and he was so impressed with her overture, that he smiled and forgave her.
At this point, we can ask some questions. What did the flowers represent? Did the flowers replace the Vase? No. Did Debbie give Father money to replace the vase? No. Did Sam give Dad money on his daughter's behalf? No. Did Dad pay for the Vase? No. Nobody paid for the vase or replaced it.
The flowers represented a peace offering in light of Debbie's contrition. She is sorry for breaking the vase. She is sorry for disobeying his proscription against running in the house. She senses that her behavior has placed emotional distance between her and her father. In her childlike way, she asks herself, "What can I do to regain my father's favor?"
Father decided to accept his daughter's peace offering and to reestablish intimacy and friendliness between himself and his daughter because he loves her. Father didn't punish anyone for what she did. He didn't punish is daughter, he didn't punish his son. He forgave her and restored the relationship for his own reasons, which weren't punitive. The flowers were the atonement offering.