The Anti-Life Equation is the conceptual power to dominate the will of any sentient race. It is among other reality altering powers that twist and distort freedom. It is called the Anti-Life Equation because "If someone possesses absolute control over you - you're not really alive."
Though the full version of the equation is barely known to any one person at one point, a full version of the Equation supposedly existed in the mind of the billionaire "Billion Dollar" Bates.
The Equation can be countered by the concepts of freedom and hope; however, the New Genesis hieroglyph of Freedom, called the Metron Emblem, significantly wears down the formula's ability to dominate other wills, allowing the infected to fight against the Equation and win while exposed to the symbol; a Metron Emblem large enough is able to massively disrupt the Anti-Life Equation's powers transmitted through various frequencies and even wear down those wearing Justifier Helmets if in the vicinity.
loneliness + alienation + fear + despair + self-worth ÷ mockery ÷ condemnation ÷ misunderstanding x guilt x shame x failure x judgment n=y where y=hope and n=folly, love=lies, life=death, self=dark side
The first sign of the Equation came about when 300 years ago when Darkseid made contact with the Martians. When he learned that Martian philosophy was based on the "Life Equation," which equals to free will, he theorized that an opposite equation must also exist.
Darkseid used clones of Billion Dollar Bates to get access to the Equation. In stopping them, Orion learned the Equation and tried to use it to make people happy and good, but realised that the supression of free will is always a bad thing.
Mister Miracle knew the full formula but possessed a willpower not to use it. However, after becoming increasingly unbalanced by the death of his wife, Big Barda, Mister Miracle decides to use the Equation.
He then becomes determined to hunt down the killer of the New Gods and comes face to face with the Source and is killed himself. It is then revealed that the Anti-Life Equation is an entity that is the dark half of the Source. Which the Source is finally reunited with.
When Darkseid became the last of the New Gods, he is faced in battle by the Source and he reveals that he had created a serum giving him power drawn directly from the Anti-Life Entity. Regardless of his boost in power, in the end Darkseid is also killed.
Though Darkseid was killed, due to his knowledge of the full equation and his will to fully use it, he made sure he was spiritually reborn in the body of a human on Earth. He becomes Boss Dark Side, but the shell is not enough to fully store him and he is eventually killed again. He then uses the spoken word to be reborn again, this time in the body of Dan Turpin. He also develops his base on Earth, using the equation to turn heroes, civilians and villains alike into mindless slaves.
Darkseid's use of the Equation is ultimately broken when Wonder Woman, herself a slave of Anti-Life, is freed of the Equation and binds Darkseid with the Lasso of Truth, breaking the Anti-Life Equation's hold on the people of Earth.
The member of Young Justice the Empress possesses pieces of the Equation, giving her limited mind control.
The Pied Piper also possesses the formula in his mind and has been using it unknowingly with his sonics. He became a pawn of Desaad in an attempt to gain the Equation to kill Brother Eye and Darkseid to rule Apokolips.