Doodle function: Difference between revisions
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The function revolves around a specific type of one-dimensional cellular automaton, in which state of a cell is determined by its own state and state of the cell to its right at previous generation (Hollom's original explanation is slightly different, but equivalent to this one). The function doodle(c,n) is then defined to be the longest time an automaton can go on without repeating the state, if we are constrained to automata with c states and initial seed of length at most n (with blank cells between non-blank cells counted). | The function revolves around a specific type of one-dimensional cellular automaton, in which state of a cell is determined by its own state and state of the cell to its right at previous generation (Hollom's original explanation is slightly different, but equivalent to this one). The function doodle(c,n) is then defined to be the longest time an automaton can go on without repeating the state, if we are constrained to automata with c states and initial seed of length at most n (with blank cells between non-blank cells counted). | ||
== | == Notation == | ||
doodle(n) = doodle(n,2) | doodle(n) = doodle(n,2) | ||
== Known values == | == Known values == | ||
Revision as of 09:39, 11 August 2025
The doodle function is a function made by Lawrence Hollom. It is a two-argument function.[1]
Definition
The function revolves around a specific type of one-dimensional cellular automaton, in which state of a cell is determined by its own state and state of the cell to its right at previous generation (Hollom's original explanation is slightly different, but equivalent to this one). The function doodle(c,n) is then defined to be the longest time an automaton can go on without repeating the state, if we are constrained to automata with c states and initial seed of length at most n (with blank cells between non-blank cells counted).
Notation
doodle(n) = doodle(n,2)
Known values
doodle(1,n) = 1
doodle(2,n) = n
doodle(3,2) ≥ 487. Hollom checked every possible setup using a computer program and all others either looped in smaller number of steps, or haven't done so in 10,000 steps. He believes that 487 is the exact value of this function.
They are no lower bounds for doodle(4,2), and doodle(5,2) yet.