What is a Fibonacci spiral?

It is a spiral formed by connecting quarter-circle arcs in squares whose side lengths follow the Fibonacci sequence (1, 1, 2, 3, 5, …). It approximates a golden (logarithmic) spiral as you add more squares.

Is this a golden spiral generator?

Yes in the usual sense: the Fibonacci spiral built from quarter circles in Fibonacci squares closely approximates the golden spiral. The tool draws that classic Fibonacci spiral and shows how ratios of consecutive Fibonacci numbers approach φ (about 1.618).

Does it work as a Fibonacci spiral calculator?

Yes: enter n to get F(n) with exact integers (BigInt), copy the value, and generate comma-separated lists of the first n terms. The canvas also labels each square and shows F_last/F_{last-1} approaching φ.

Is there Fibonacci spiral ASCII art?

Yes: the ASCII preview matches the same tiling and spiral in monospace text (digits in squares, asterisks on the spiral). Copy it for terminals, docs, or social posts. For high-resolution art, use PNG export.

How is the spiral drawn?

Squares are placed in the standard Fibonacci tiling pattern. Each arc is a quarter circle with radius equal to the square side; the center is the square corner closest to the spiral pole (the corner shared by the first two 1×1 squares), so the arc stays inside the square and meets the next arc smoothly.

Fibonacci Spiral Generator Free Online

Free Fibonacci spiral generator and golden spiral preview, Fibonacci calculator (F(n) and first-n terms), ASCII art text you can copy, Fibonacci numbers on squares, live φ ratio, colors, and PNG export.

Spiral controls — preview updates live.

Squares (10)

More squares → larger Fibonacci sizes.

Scale

Colors

Spiral arcs Numbers on squares Grid lines

Fibonacci calculator F(n) & sequence

F₁=1, F₂=1, …

F₁₂ = 144

First 12 terms

ASCII text export

Monospace raster; wider = more detail.

Width (chars)

Live preview

Scroll up/down to zoom · Drag to pan · Double-click resets pan · Square sides follow Fibonacci 1, 1, 2, 3, …

ASCII preview (optional)

How it works

Fibonacci numbers start with 1, 1, then each term is the sum of the two before: 1, 1, 2, 3, 5, 8, 13, …

Tiling packs squares with those side lengths along a rectangle in a fixed order (add to the right, then below, then left, then above, and repeat).

Spiral In each square, a quarter circle of radius equal to the side length is drawn with its center at the corner nearest the spiral pole (where the first two 1×1 squares meet), so each arc stays inside its square and joins the next; this approximates the golden spiral. Ratios of consecutive Fibonacci numbers approach φ ≈ 1.618.

φ = (1 + √5) / 2
F_n+1/F_n → φ as n grows

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