Encyclopedia/All topics/Patterns

Patterns

Articles 1–28 of 28. Alphabetical by title.

• 06Gray cycle

• Patterns

  Patterns are the finite bit strings a recognition cycle can visit, and the module proves the shortest complete visit takes exactly 2^d ticks.

• Patterns Cover Exact Pow

  A simple counting proof shows that a sequence of on-off patterns can visit every possibility in exactly 2^d steps, no more and no fewer.

• Patterns Gray Code

  Gray code is a way to list every binary pattern so that consecutive patterns differ in only one bit, and the framework uses it to order the discrete states a recognition ledger can

• Patterns Gray Code Axioms

  A Gray code is a way of ordering binary numbers so that consecutive values differ by a single bit, a classic tool in digital circuits.

• Patterns Gray Code Axioms Gray Code One Bit Property

  A Gray code is a way of ordering binary numbers so that consecutive values change in only one bit, and the framework's machine-checked library records that fact as a formal th

• Patterns Gray Code Axioms Gray To Nat Inverts Nat To Gray

  The binary-reflected Gray code, a way of ordering numbers so consecutive values differ in one bit, has a known inverse; the framework's library states this as a formal theorem

• Patterns Gray Code Axioms Gray To Nat Preserves Bound

  A Gray code is a binary sequence where consecutive values differ by one bit; the bound theorem says that converting such a code back to a number never overflows its bit width.

• Patterns Gray Code Axioms Nat To Gray Inverts Gray To Nat

  A Gray code is a way of ordering binary numbers so consecutive values differ by a single bit; the framework's library records that the standard conversion back and forth is ex

• Patterns Gray Code Binary Reflected Gray

  A Gray code is a way to count through binary numbers by changing only one bit at a time, and the binary-reflected construction is the classic recipe for building one.

• Patterns Gray Code Gray To Nat

  Gray code lets adjacent binary numbers differ by a single bit; grayToNat is the function that undoes that encoding.

• Patterns Gray Code Nat To Gray

  Gray code is a way to order binary numbers so consecutive values differ by a single bit, a trick used in rotary encoders and error correction.

• Patterns Gray Cycle Brgc

  A Gray cycle is a loop through every binary pattern of a given length, changing exactly one bit per step; the BRGC construction builds one for any dimension without assuming any ax

• Patterns Gray Cycle Brgc Brgc One Bit Step

  A Gray code is a way to list binary strings so that each entry differs from the last by a single bit, and this theorem shows a standard construction always has that property.

• Patterns Gray Cycle Brgc Brgc Path Injective

  A Gray code lists every binary pattern exactly once, changing one bit at a time; a machine-checked proof shows one standard construction never repeats itself.

• Patterns Gray Cycle Brgc One Bit Diff Snoc Bit Flip

  A small lemma about appending a bit to a binary pattern proves a key step in building Gray codes, the sequences where consecutive entries differ by one bit.

• Patterns Gray Cycle Brgc One Bit Diff Snoc Bit Same

  A small lemma about Gray codes says that appending the same bit to two patterns preserves their one-bit difference, a property that makes the recursive construction of Gray cycles

• Patterns Gray Cycle General

  A Gray code is a way to list binary strings so each step changes only one bit; Recognition Science proves such a list exists in every dimension.

• Patterns Gray Cycle General Brgc Wrap One Bit Diff

  A Gray code lists binary patterns so consecutive entries differ in one bit; the wrap-around step closes the list into a cycle.

• Patterns Gray Cycle General Exists Gray Cover Of Le64

  A Gray code is a way to list binary strings so that each step changes exactly one bit; the framework proves such a list exists for any size up to 64 bits.

• Patterns Gray Cycle General Exists Gray Cycle Of Le64

  A machine-checked theorem guarantees that any dimension up to 64 admits a Gray cycle, a path through all binary patterns that changes one bit at a time.

• Patterns Gray Cycle Gray Cover Eight Tick Min

  A machine-checked theorem proves that visiting all eight three-bit patterns, one bit at a time, requires at least eight steps.

• Patterns Gray Cycle Gray Cycle3 Bijective

  A Gray code is a way to list all eight three-bit strings so that each step changes exactly one bit; the framework proves such a list exists and forms a closed loop.

• Patterns Gray Cycle Gray Cycle3 One Bit Step

  A Gray code is a way to list all 3-bit binary strings so that each step changes exactly one bit, and the framework's library proves the classic 8-step cycle exists.

• Patterns Gray Cycle Gray Cycle3 Surjective

  A Gray code lists all binary strings of a given length so that consecutive entries differ in exactly one bit; here is the machine-checked proof for three bits.

• Patterns Min Ticks Cover

  How many steps must a listing take before it can show every possible pattern? The answer is exactly two to the power of the pattern's bit count.

• Patterns T7 Nyquist Obstruction

  To tell every possible pattern of D bits apart, at least 2^D distinct samples are needed; fewer samples force two patterns to collide.

• Patterns T7 Threshold Bijection

  A simple counting fact about binary patterns: with exactly 2^D time slots, every D-bit pattern appears exactly once, a result the Recognition Science framework proves and links to