Yes it does, depending on the design. It becomes somewhat larger in some designs and various rods are added to the to the ends of the antenna parallel with and inline with the elements. Rods are added behind the elements to act as reflectors to increase the gain and make the antenna uni-directional (gain in one direction only).
For a given size it will not have as much high band VHF gain as it does UHF gain, but some may still have 6 dBd to 8 dBd gain relative to dipole antenna. This is gain with out the noise that an amplifier will add.
This may or may not be enough to help with your issues.
Once again, in case it has been missed I will recommend
TV FOOL.
In general you need at least -80 dBm at the antenna terminal of the TV with a carrier to noise ratio of at least 15 dB. This will vary from set to set.
This is where the noise factor of the amplifier comes into play. You may have a signal that is just slightly too weak and just on the threshold of an acceptable carrier to noise ratio. The amplifier will make the signal larger, but it will degrade the carrier to noise ratio.
Using the information in the chart for your location from TV FOOL, you can approximate the amount of gain you may need for the stations that are difficult to receive.
BTW here are a couple of active links on AK, our sister site, discussing the Hoverman style antenna and the fractal style antenna.
Basic antennae
Fractal antennae
It appears that some of the designs of the fractal antenna, such as the Koch Curve fractal geometry antenna work well at UHF frequencies and some have reported operation at VHF frequencies.
It is somewhat difficult to model the various fractal antenna designs as found on the internet, because of the unique manner in which some of the builders interweave the various elements of this the antennae.
I have modeled the Hoverman style antenna in software using this
4nec2 software.
Here is the performance of a Hoverman style antenna at 175 Mhz, the frequency for channel TV channel 7 (first picture). The performance of this version of the Hoverman style antenna if fairly constant with increasing gain and decreasing beam width (more directional) as the frequency increases.
Its performance falls apart below about 150 Mhz and is very poor in the FM broadcast band. See the second picture, the pattern resembles the pattern for a dipole antenna, but with slightly less gain.
In the third picture you can see its performance in the UHF band.
14.6 dBi which is about 12 dBd, that is gain over a dipole antenna.
This is the result of software modeling, but in my case measured performance came close to the modeled results.
Look at the lower right side of the picture, the gain is 9.46 dbi which equals about 7 dBd, gain over a dipole antenna.
I lost some files recently and no longer have the specifics about this antenna.
Because the Fractal antenna is heavily patented, there is very little technical information available from the inventor or his company.
There is some second hand information, but it is not consistent.
The Koch Curve fractal geometry fractal antenna seem to be popular because it is easy to construct, the bends in the wire are basic triangular bends.
The last 2 pictures show the basic form of the Koch Curve fractal geometry fractal antenna. Note there is considerable is variation on the dimensions and the shape of the basic self similar form in the designs.
I can not speak to these designs in terms of hard numbers for VHF TV band operation. As I have mentioned I had computer issues and lost files of information containing the data relative the element for some variations of this antenna. Each of the more complex antennae may have to have several hundred points of data describing the element segments used by the software.
Feel free to experiment and relay your results to us. A little solid copper wire and a form to bend the wire around and you will be good to go.
By the way the impedance of the Hoverman style antenna remains close to 300 Ohms from 175 Mhz through 800 Mhzz
Some of the various designs of the Koch Curve fractal geometry fractal antenna have feed point impedances that vary from the standard 300 Ohms.
Remember RF is the acronym for "Really Fun".
If you have additional questions, I will try to answer them.
Good luck with your quest for perfect reception, and with OTA digital TV reception it must be perfect or all is not good.
My meds are affecting me, I forgot one of the pictures. The last picture, taken from the internet due to my lost files, is how the antenna is modeled starting with a very simple version. Every time the overall shape of the self same iterations is changed, it requires changing the data in the software to model the antenna.
The other antenna performance graphs are from my files.