Apophenia

What it is

Perceiving connections or meaning in unrelated things, such as faces in clouds or omens in coincidences.

Example Reading a hidden message in a random sequence of numbers.

Post hoc ergo propter hoc fallacy
Seeing a causal link between two unconnected events is apophenia, the perception of meaning in coincidence.
Clustering illusion bias
Both find patterns in randomness; the clustering illusion does it for data, apophenia for any stimuli.
Coincidences and unlikely events bias
Reading meaning into coincidences is apophenia.
Forer effect bias
Both attach meaning to the meaningless: patterns in noise, personal relevance in generic statements.
Texas sharpshooter fallacy fallacy
Drawing the target around random hits is a form of apophenia: finding a pattern in noise.