Fractional Bsplines  
The animation shows the fractional Bsplines with an α that runs from 0 to 5. 

QuickTime or MPEG 
QuickTime or MPEG 

Note that these are valid scaling functions for all α >1/2.  
Symmetrized fractional Bsplines  
The animation shows the symmetrized fractional Bsplines with an α that runs from 0 to 5. 

QuickTime or MPEG 

Reference: M. Unser, T. Blu, "Fractional Splines and Wavelets," SIAM Review, vol. 42, no. 1, pp. 4367, March 2000. 

Fractional Bspline wavelets  
The animation shows the fractional Bspline wavelets with an α that runs from 0 to 5. 

QuickTime or MPEG 
QuickTime or MPEG 

Note that every single wavelet on this graph generates a stable wavelet basis of L_{2 }(the space of finite energy functions).  
References: M. Unser, T. Blu, "Fractional Splines and Wavelets," SIAM Review, vol. 42, no. 1, pp. 4367, March 2000. M. Unser, T. Blu, "Construction of Fractional Spline Wavelet Bases," Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing VII, Denver CO, USA, July 1923, 1999, vol. 3813, pp. 422431. 