Generate Fibonacci sequences to any length with golden ratio visualization and spiral drawing on canvas.
Type a length and this page returns the Fibonacci sequence as a numbered list: each term is the sum of the two before it. Alongside the list it shows how the ratio of consecutive terms closes in on the golden ratio, and it draws the classic spiral on a canvas by fitting quarter-circle arcs into squares whose sides are the Fibonacci numbers. The surprise most users hit first: there are two conventions, starting with 0, 1 or with 1, 1, so the same length produces two different lists. The sequence also outgrows practical sizes quickly: term 50 is 12,586,269,025.
A concrete input and expected output from the current implementation.
Input
16 terms
Expected output
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610
Each new term is the sum of the two before it, so the sixteenth term is 233 + 377 = 610. With the alternative 1, 1 start, the sixteenth entry would instead be 987, which is why confirming the starting pair matters.
With the 0, 1 start, the page builds the list term by term: each entry after the first two is the sum of its two predecessors, so the sequence runs 0, 1, 1, 2, 3, 5, 8, 13 and on. The recurrence is the whole definition; the values need no other formula. Because the addition compounds, the sequence grows exponentially, roughly by the golden ratio each step.
Dividing each term by its predecessor gives ratios that alternate above and below the golden ratio, phi = (1 + sqrt(5))/2, about 1.618, converging closer with every step. The canvas visualization tiles squares with side lengths equal to consecutive Fibonacci numbers and connects quarter-circle arcs of those radii; the joined arcs approximate a logarithmic spiral, the shape often called the Fibonacci or golden spiral.
Not exactly. The drawing fits quarter-circle arcs into squares whose sides are Fibonacci numbers, so the curve changes radius in steps at each arc boundary. A true golden spiral is a single continuous logarithmic curve whose radius multiplies by phi every quarter turn. The two look nearly identical, and the drawn version converges to the true shape as the sequence grows, but they are not the same curve.
With the 0, 1 convention, the value at index 100 is 354,224,848,179,261,915,075. Because each step multiplies the size by roughly the golden ratio, the index-100 value runs to 21 digits, so long sequences legitimately look enormous. If your result for that position ends in zeros or falls short of 21 digits, precision loss is the cause and exact arithmetic is needed.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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