Calculate Dragon Curve Numbers

This tool calculates the binary sequence behind the dragon curve, a classic fractal pattern. Each term is built by flipping and appending the previous string in a recursive way. You start with “1”, then each step adds a 1 and a flipped (bit-inverted + reversed) version of the current sequence. It’s a fascinating structure that grows fast and reveals self-similar patterns.

You can control how the output appears, copy it instantly, or download the list to use elsewhere.

Total items: 0
Options
Line-by-line output
Show index numbers

How to Use:

  1. Enter how many dragon curve terms you want to generate.
  2. Use the toggles to change layout:
    • Line-by-line or inline formatting
    • Index numbers ON or OFF
  3. The preview updates instantly every time you change a setting or input.
  4. Click “Copy Output” to copy the result to your clipboard.
  5. Click “Export to File” to save the full list.
  6. Click “Clear All” to reset everything to default.

What Calculate Dragon Curve Numbers can do:

Each term follows the rule:Sₙ = Sₙ₋₁ + ‘1’ + reverse(flip(Sₙ₋₁))

This tool does all the heavy lifting for you, building the binary sequence step-by-step. It supports dynamic formatting, lets you see how the sequence evolves, and highlights each output change with a flash. The index toggle is handy for tracking iteration steps, especially when using the data in visual generators or logic experiments.

You’ll also see a counter that shows exactly how many items were generated.

Example:

Input:

4

Settings: Line-by-line: ON, Show index: OFF

Output:

1
110
1101100
110110011100100

Common Use Cases:

Great for exploring fractals, binary-based recursion, or algorithmic pattern growth. This tool helps students visualize string evolution and gives developers a fast way to pull dragon curve data for art, games, or simulations. Whether you’re analyzing structure or just playing with bit flips, it delivers results instantly.

Useful Tools & Suggestions:

If you’re diving into patterns like the dragon curve, Generate Polynomial Sequence is useful for building structured progressions. And when you want to see how digits behave in a more chaotic way, Find Entropy of a Number gives you a peek into randomness.

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