Butterfly effect

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 in that travelling to the past and making any little change, even something like crushing a butterfly, could drastically change the future. The Twelfth Doctor cited the "ripple effect," stating that if he'd change the past he could create a future where cats ruled the universe. (TV: Before the Flood)

The Fourth Doctor accidentally stepped on a butterfly once but didn't notice it. (PROSE: Prelude Falls the Shadow)

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) While in the year 1993, Romulus Terrin, who was from the year 2381, assured James Rafferty that he was not going to go treading on any butterflies. (PROSE: The Dimension Riders) 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 few 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)

A literal example of the butterfly effect was regularly caused by the Council of Eight when they tried to fill the void left by the Time Lorda after they were wiped out. The Council regularly dispatched their Time Agents through time corridors to set moments in order to ensure predicted outcomes in history came to pass. In one case, a Time Agent released a butterfly in the atmosphere in a location in Africa, which resulted in changes to the atmosphere which led to the sinking of the Spanish Armada. (PROSE: Sometime Never...)

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 "[not to] step on any butterflies", and asked her, "What have butterflies ever done to you?" (TV: The Shakespeare Code)

When Bill Potts asked about the butterfly effect, the Twelfth Doctor teased her by inventing a friend of hers, "Pete", who had stepped on a butterfly and accidentally erased himself from existence. (TV: Thin Ice)

A chaotic limiter could be used to reduce or increase the butterfly effect. (PROSE: The Book of the War)