Dragon Curve Generator

Fold a strip of paper once, then again and again, always folding the same way, until the strip is a compact packet. Open every crease to a right angle and the strip traces a shape that doubles its complexity with each fold - the dragon curve, discovered in 1966 by three NASA physicists doodling with paper, and named for the sinuous outline it draws. The open direction of every crease follows a fixed infinite pattern: the one-sided paperfolding sequence 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1...

Dragon Curve Generator computes the paperfolding sequence by its fold recurrence - even positions mirror earlier terms, odd positions alternate - and shows every term as a digit and as a turn: 1 means a right turn, 0 a left turn, the instructions a turtle would follow to draw the curve. Choose a start index and a count; copy or download the run as index, digit and turn rows.

• Exact fold recurrence: Terms computed from a(2n) = a(n) and alternating odds - no randomness, no rounding.
• Digit and turn on every row: One and zero become R and L, the dragon walking directions.
• Start anywhere: From index 1 to ten million, any run of up to 20,000 terms.
• Turn balance stats: The right minus left tally shows the walk drifting back toward zero.
• Copy or download: One click export of the whole run as index, digit, turn lines.
• Reference tab: The fold-to-digits story, the turning interpretation, the fractal family.
• Free and private: All generation runs locally - nothing is uploaded, stored or logged.

1. Set the start index - which term of the fold to begin with (1 to 10,000,000).
2. Set the count - terms to generate, up to 20,000.
3. Generate - the recurrence fills the run in one pass.
4. Read digit and turn - 1 with R, 0 with L, on every row.
5. Copy or download the run for plotting, teaching or further analysis.

Example 1 - The first folds. Generate 8 terms: 1, 1, 0, 1, 1, 0, 0, 1 - the creases of a strip folded three times. Walk them as trades: R, R, L, R, R, L, L, R.

Example 2 - A doubling. Generate 16 terms and compare rows 9 to 16 with rows 1 to 8. The first 8 recur mirrored inside the second 8 - the self-similarity of the fractal starts at the very beginning.

Example 3 - Manhattan walking. Generate 32 terms and plot the turns on graph paper from the grid in any direction: RLLR in the middle retraces... the path never crosses itself; the dragon tiles the plane at every stage.

Example 4 - The balance. Generate 20,000 terms and read the stats: total right turns minus left turns stays small - the walk ends far closer to a straight line than its length suggests.

Example 5 - Stretching the run. Start at index 1,000,000 and count 100 terms: the recurrence delivers the millionth fold instantly - a stretch of infinite sequence with no seed list.

• True sequence: The genuine paperfolding numbers, no simulation and no approximation.
• Two readings at once: Digit and turn side by side make the paper and the turtle view one table.
• Any stretch: Starting late in the infinite fold costs nothing extra.
• Self-similarity visible: Blocks of powers of two show the doubling rule directly.
• Clean export: Copy or download lines ready for plotting software or class handouts.
• Private and free: Everything stays in the browser; nothing is uploaded or logged.