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deleted 49 characters in body

edited Oct 12, 2014 at 21:23

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RecurrenceTable:

RecurrenceTable[{ x[n + 1] == x[n] + (1/2) (Sqrt[1 - y[n]^2] - x[n]), y[n + 1] == y[n] + (1/2) (Sqrt[1 - x[n]^2]x[n + 1]^2] - y[n]), x[0] == 0, y[0] == 0 }, {x, y}, {n, 1, 105}] // N

{{0.5, 0.5}, {0.683013, 0.683013}, {0.70671, 0.70671}, {0.707107, 0.707107}, {0.707107, 0.707107433013}, {0.707107700694, 0.707107573237}, {0.707107, 0.707107}760042, {0.707107, 0.707107611556}, {0.707107775621, 0.707107621377}, {0.707107779567, 0.707107623848}}

Credit goes to Stelios for spotting a mistake in the original answer :)

RecurrenceTable:

RecurrenceTable[{ x[n + 1] == x[n] + (1/2) (Sqrt[1 - y[n]^2] - x[n]), y[n + 1] == y[n] + (1/2) (Sqrt[1 - x[n]^2] - y[n]), x[0] == 0, y[0] == 0 }, {x, y}, {n, 1, 10}] // N

{{0.5, 0.5}, {0.683013, 0.683013}, {0.70671, 0.70671}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}}

RecurrenceTable:

RecurrenceTable[{ x[n + 1] == x[n] + (1/2) (Sqrt[1 - y[n]^2] - x[n]), y[n + 1] == y[n] + (1/2) (Sqrt[1 - x[n + 1]^2] - y[n]), x[0] == 0, y[0] == 0}, {x, y}, {n, 1, 5}] // N

{{0.5, 0.433013}, {0.700694, 0.573237}, {0.760042, 0.611556}, {0.775621, 0.621377}, {0.779567, 0.623848}}

Credit goes to Stelios for spotting a mistake in the original answer :)

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answered Oct 12, 2014 at 20:13

C. E. ♦

71.7k
7
144
279

RecurrenceTable:

RecurrenceTable[{ x[n + 1] == x[n] + (1/2) (Sqrt[1 - y[n]^2] - x[n]), y[n + 1] == y[n] + (1/2) (Sqrt[1 - x[n]^2] - y[n]), x[0] == 0, y[0] == 0 }, {x, y}, {n, 1, 10}] // N

{{0.5, 0.5}, {0.683013, 0.683013}, {0.70671, 0.70671}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}, {0.707107, 0.707107}}