OK, so time for me to chime in here.
I am sorry to be the bringer of bad news, but fractal antennas offer no real advantage over any properly matched and tuned antenna. There have been a couple of nutters out there trying to push fractals as a more efficient antenna. What they might do, and the jury is still out, is provide a an antenna with a wider match across frequencies. Their claim to be as efficient as larger antennas but in a smaller package is normally "proven" using some pretty shaky testing procedures.
If you look up fractal antennas you wil find wikipedia has an article in it referring to the work of a Nathan Cohen. He is a regular nutbar who just happened to spend many hours arguing with people on usenet groups about antennas. He provided anecdotal evidence as proof for his designs being effective. Never once did he provide anything other than woowoo claims. If you want to believe that because he has a patent that the concept and design must be worthy, think again. The patent process is a broken pile of garbage. it does not meant that anything has any merit anymore.
Fresnel antennas use a method of destructive and constructive interference from waves passing though concentric circles of conductive material to form a hot spot at the "focus" They are not particularly efficient. They have nothing to do with fractal junk.
The connection of two antennas together with a proper impedance cable will result in a passive repeater, but...
The cable or connection between the two antennas will have loss and that should be taken into account. Also the two antennas will have their own losses. It is possible to make a passive repeater this way but it needs to use the least amount of interconnecting and least lossy wire/cable in between them. The best antennas to do this would be Yagis, or dishes, to provide the highest gain at each end.
In the case of the original poster, it is probably best to make a high tower, or make a remote antenna and receiver and have it feed the house with the baseband signal using high quality coax and amplifiers.
There is no free lunch when it comes to things like this.