  We have studied several generalizations of Fibonacci sequences as the
sequences with arbitrary initial values, the addition of two and more Fibonacci
subsequences and Fibonacci polynomials with arbitrary bases. For Fibonacci
numbers with congruent indices we derived general formula in terms of
generalized Fibonacci polynomials and Lucas numbers. By extending Binet formula
to arbitrary real numbers we constructed Binet-Fibonacci curve in complex
plane. For positive numbers the curve is oscillating with exponentially
vanishing amplitude, while for negative numbers it becomes Binet Fibonacci
spiral. Comparison with the nautilus curve shows quite similar behavior. Areas
under the curve and curvature characteristics are calculated, as well as the
asymptotic of relative characteristics. Asymptotically for n going to infinity
the region become, infinitely wide with infinitesimally small height so that
the area has finite value $A_{\infty}=\frac{2}{5 \pi} ln(\varphi)$.
