Constant Wire Comparisons(a stylistic note: all graphics in the table below link to full displays) This survey reveals that taking a length of wire and applying almost any folding to it will allow it to retain its spectrum of resonances. By this I mean that it will resonate at intervals roughly matching the resonances of the monopole it is derived from. 64 MetersThe table that follows contains Reference and Fractal Antennas SWR spectrums for designs consuming 64 meter of wire. It should be noted that due to the manner in which wire is consumed (bent and turned away from the vertical, or reversed), all fractals are much smaller than 64 meters tall. Observe also that the smaller fractal antennas produce nearly as many resonances as the large radiator. The interesting trend displaying separable features is found in three fractals, the Triadic, MB Curve, and ZFold, showing progressive smoothing of their high Z SWRs in the upper band. The relationships displayed here are a onetoone correlation of this trend with complexity. 
Reference 64 meter tall Radiator SWR 

32 Curve 2nd Order 50 Ohm SWR 

Triadic Koch 2nd Order 200 Ohm SWR 

MB Curve 2nd Order 200 Ohm SWR 

ZFold 2nd Order 200 Ohm SWR 

Quadratic Koch 2nd Order 200 Ohm SWR 
In the following table I have many of the antenna designs above scaled to 16 meters of wire. As always, the first entry is a reference: the 16 meter tall monpole driven against a perfect ground. The remaining entries all consume 16 meters of wire in tracing the fractal shape also driving against a perfect ground. The net result is that each fractal is significantly lower than the standard monopole. The table entries are at SWR minima, a 50 Ohm match is not rare, but byandlarge some minor matching will be required.
The table columns described as x , x element length, H and ordering factor all relate to the physical dimension. x is the number of unit length elements in the first order form. For the monopole it is simply one unit length (the unit being 16 meters). H as you may guess is height to the top of the vertical antenna. You may also note that some fractals have the same x but not the same H. In order to separate out the various designs, the application of H times element length yields my ordering factor.
indicated value is in terms of (resonant frequency in MHz) * (resonant length in Meters)
to find the length of wire in Meters required for resonance, take indicated value and divide by that resonant frequency in MHz
Second Order 
x 
x element length 
H 
ordering factor 
160M 12 
80M 24 
40M 48 
30M 812 
20M 1216 
17M 1620 
15M 2024 
12M 2428 
10M 2832 
3236  3640  4044  4450 
16 meter Standard 
1 
1.00 
16 
16 
72.96  222.4  371.2  521.6  671.9  
Sierpinski 
2 
0.50 
8.5 
4.25 
78.40  232.0  390.4  537.6  688.0  
32 Curve 
3 
0.33 
7.0 
2.31 
87.68  251.2  404.8  553.6  707.2  
Koch Triadic 
4 
0.25 
9.0 
2.25 
86.40  249.5  407.2  566.4  718.5  
MB Curve 
5 
0.20 
5.7 
1.14 
97.60  267.2  427.2  580.8  720.0  
ZFold 
5 
0.20 
4.0 
0.8 
93.60  265.6  429.6  589.6  755.2  
Koch Quadratic 
8 
0.125 
4.0 
0.5 
107.2  286.4  449.6  622.4  798.4 
On the basis of the surveys conducted and presented above, the following "special wire equations" for length of wire consumed in various low SWR antennas have been determined:
First SWR null (0.25 wavelength)
(73 + (1.20 * x)  (0.010 * x^{2})) / (F_{0})
Second SWR null (0.75 wavelength)
(220 + (2.35 * x)  (0.020 * x^{2})) / (F_{0})
Third SWR null (1.25 wavelength)
(371 + (3.10 * x)  (0.030 * x^{2})) / (F_{0})
Fourth SWR null (1.75 wavelength)
(520 + (3.30 * x)  (0.025 * x^{2})) / (F_{0})
Fifth SWR null (2.25 wavelength)
(670 + (3.30 * x)  (0.015 * x^{2})) / (F_{0})
The variable x in all equations is for the number of sections in the structure (corresponding to wires in EZNEC and not segments). These solutions are the best fit to the data provided above and are not suitable for fractal comparisons where the number of elements in any fractal exceeds 50.