My Favourite (Math) Mistake 
We often think that to be a mathematician we are supposed to be a genius (hence not make mistakes), but that couldn't be further from the truth! Have a look at this video of a discussion between students and faculty about our favourite mistakes to find out more about the issue, including pre and postcognition, the impostor syndrome, the prodigy myth, defining variables to be themselves, being a human in math, and other interesting stuff! 
The family of curves y^2 = (x+1)(x^2+c) for c=0.5,...,0.5  
The Mandelbrot Fractal: For complex c, the recursion z[n+1] = z[n]^2 + c; f(z) = exp(Mod(z)) is plotted for n=1,2,...,20, with z[0] = 0+0i. 

The SwendsenWang algorithm (right) mixes faster than the Gibbs sampler (left) for sampling the Ising model (attraction parameter 0.9)  
Diffusion Limited Aggregation (first 12000 of 50000 particles on a 400 x 400 grid within radius 200) 