https://ncg777.github.io/sequence-operator/

Merge in the Patch view (2026.9.30)

Add Merge from the Combine palette group (or search for “merge” or “interleave”). Wire sequences into x and y, then connect out to a Display or another node. Merge has no Combiner or Operation selector.

The result alternates elements, starting with x. Both inputs repeat until they complete a common cycle, producing 2 × LCM(length(x), length(y)) elements:

• 1 2 3 merged with 4 5 6 → 1 4 2 5 3 6
• 1 2 merged with 7 8 9 → 1 7 2 8 1 9 2 7 1 8 2 9
• 1 2 3 merged with 9 → 1 9 2 9 3 9

Merge waits for both inputs. An empty sequence produces an empty result. Use Append to join whole sequences end to end. Merge works in saved programs and subprograms with the existing graph format.

Polynomial indices

The P(x) dialog samples the result sequence at (d*x³ + a*x² + b*x + c) mod n, where n is its length. It shows Permutation when every position is used exactly once, or Not a permutation when positions repeat or are skipped. Both can be applied, and any sequence length is supported. Leave d = 0 for the existing quadratic behavior. The Patch node also has an optional d input; existing saved quadratic nodes continue to work.

CLI

Build the tools first:

yarn build-tools

Then use the sequence-operator command:

# Combine two sequences
node dist-tools/cli.js combine -x "1 2 3" -y "4 5 6" -c Product -o Add
# → 5 6 7 6 7 8 7 8 9

# Merge two sequences (no combiner or operation required)
node dist-tools/cli.js merge -x "1 2" -y "7 8 9"
# → 1 7 2 8 1 9 2 7 1 8 2 9

# Reverse a sequence
node dist-tools/cli.js reverse -s "1 2 3 4 5"
# → 5 4 3 2 1

# Rotate a sequence
node dist-tools/cli.js rotate -s "1 2 3 4 5" -n 2
# → 4 5 1 2 3

# Cyclical difference
node dist-tools/cli.js cyclical-difference -s "0 1 3 6 10"
# → 1 2 3 4 -10

# Cyclical antidifference
node dist-tools/cli.js cyclical-antidifference -s "1 2 3 4" -k 0
# → 0 1 3 6

# Difference
node dist-tools/cli.js difference -s "0 1 3 6 10"
# → 1 2 3 4

# Antidifference
node dist-tools/cli.js antidifference -s "1 2 3 4" -k 0
# → 0 1 3 6 10

# Signs
node dist-tools/cli.js signs -s "-3 0 5 -1 2"
# → -1 0 1 -1 1

# ax²+bx+c
node dist-tools/cli.js polynomial -s "0 1 2 3 4 5 6 7" -a 1 -b 1 -c 0
# → 0 2 6 4 4 6 2 0

# Cubic: x³ modulo 5 (a permutation)
node dist-tools/cli.js polynomial -s "0 1 2 3 4" -a 0 -b 0 -d 1
# → 0 1 3 2 4

# Permute blocks
node dist-tools/cli.js permute-blocks -s "1 2 3 4 5 6" -p "2 0 1"
# → 5 6 1 2 3 4

# Unary tritwise
node dist-tools/cli.js unary-tritwise -s "1 -1 0 2 -2" -o Not
# → -1 1 0 -2 2

# Hierarchical permute (CDBHP)
node dist-tools/cli.js hierarchical-permute -s "0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15" -c "1 2 1" -p "2 0 1"
# → 0 2 4 6 8 10 12 14 1 3 5 7 9 11 13 15

# Permutation orbit
node dist-tools/cli.js permutation-orbit -s "1 2 0"
# → 3 4 -5

Run node dist-tools/cli.js --help or node dist-tools/cli.js <command> --help for the full list of options.