Simulation details: The SLE trace is simulated for the time interval [0,1]. What is plotted is actually a curve although it is impossible to follow the curve for the larger values of kappa. The Brownian motion driving function is approximated by a function which agrees with the Brownian motion at a discrete set of times. In between these times the approximating function is chosen so that the Loewner equation has an explicit solution. We choose it so that the corresponding conformal map produces a tilted slit in the upper half plane. If one takes the discrete set of times to be uniformly spaced, the simulation does poorly for the larger values of kappa. We choose the times in an adaptive way using a Brownian bridge so that the resulting points on the SLE trace are roughly uniformly spaced. (Steffen Rohde, private communication). Computing the points on the SLE trace requires evaluating the composition of a large number of conformal maps. A trick for speeding this up may be found in A fast algorithm for simulating the chordal Schramm-Loewner evolution, T. Kennedy

Plotting windows : For a given Brownian motion sample, the same plotting window is used for all of the values of kappa. For different Brownian motion samples the plotting window has the same size, but it may be shifted left or right. (One can see the position of the origin change for different samples.)