Constructing unifractal cartoons is not difficult, but it does require one bit of care. |
The generator starts at |
dt1 + dt2 + dt3 = 1     (a) |
dY1 + dY2 + dY3 = 1     (b) |
If we also impose the unifractal scaling condition |
|dYi| = (dti)H |
and take into account that the generator segments should go up, then down, then up, relation (b) becomes |
(dt1)H - (dt2)H + (dt3)H = 1     (c) |
Finally, solving relation (a) for dt3 and substituting into (c) gives the unifractal scaling condition |
(dt1)H - (dt2)H + (1 - dt1 - dt2)H = 1 |
Once we specify the coarse Holder exponent H and the interval dt1, only one value of dt2 satisfies the scaling condition. |
Moreover, the scaling condition requires |
Return to Unifractal Cartoons.