DS[t_, a_: 1, b_: 0] := Module[{u = t*3, h}, If[1 <= u <= 2, 1/2, DS[t, x_: 0, y_: 0] = (DS[t, s1_: 1, s0_: 0] = (b - s0)/(s1 - a); h = Floor[u/2]/2; DS[u - 4*h, a/2, b + a*h]/2 + h)]] E.g.; In[176]:= DS[3/13] Out[176]= 2/7 In[178]:= DS[.1] Out[178]= 3435973837/17179869184 In:= %-(1+2^-34)/5 Out= 0 My tutor Julian suggests 4*DS[x]-3*x as a continuous map of [0,1] onto [0,1] which preserves both endpoints and has slope -3 A.E. For good measure, it does this twice. (http://gosper.org/devil.png). It's tough to keep that guy's hands off my keyboard. But then why would I? (http://gosper.org/rosewindow.png) --rwg