A few examples of what you can ask Wolfram|Alpha about:
Line Replacement Fractals
draw a fractal based on iterated line replacement
draw fractals based on replacement of shapes
draw fractals by repeatedly adding smaller figures
Nowhere Differentiable Functions
plot an approximation to a nowhere-differentiable function
evaluate a nowhere-differentiable function at a point
Space-filling Curves
plot an approximation to a space filling curve
specify the number of iterations to use
plot a Julia set
plot the Mandelbrot set
plot the multibrot set of exponent d
Fractals in 3D
draw the Sierpinski tetrahedron
draw the Menger sponge
Other Fractals
plot a curlicue fractal