The butterfly effect was a theory that a butterfly could flap its wings in one place and greatly affect events in another place. (PROSE: Transit) This was a concern in time travel that travelling to the past and crushing a butterfly could drastically change the future.
The Seventh Doctor often cited this effect (AUDIO: The Dark Flame), describing butterflies as a "million multi-coloured pieces of time" and being called himself "the butterfly." (AUDIO: The Fearmonger) According to one account, he described the butterfly effect to Ingiger. (PROSE: The Curse of Fenric) He later realised that, like that theoretical butterfly, his interference in Earth's history had resulted in Kadiatu Lethbridge-Stewart learning who he was and discovering time travel. (PROSE: Transit) Ace told Sesehset about the butterfly effect while in Egypt. (PROSE: Set Piece) After a game of chess with Oskar Steinmann, the Doctor described the butterfly effect to him. Steinmann thought the solution would be to kill all the butterflies, or make them flap their wings only when ordered. (PROSE: Just War)
The Eighth Doctor confused the theory a several times, mentioning how a bat flaps its wings and causes a tropical storm (AUDIO: Invaders from Mars) and how the beat of a butterfly's wings in Mettula Orionsis caused a time storm in the Mutter's Spiral. (AUDIO: Storm Warning)
Martha Jones recognised this theory from its appearances in Earth films, and was concerned about whether or not it was safe to "move around and stuff" in her past, recalling that "You step on a butterfly, you change the future of the human race." The Tenth Doctor advised her "don't step on any butterflies", and asked her, "What have butterflies ever done to you?" (TV: The Shakespeare Code)