Man! That first picture is so out of focus that it can give you a headache... ;-)
So, looking at the second photo ('ant_top') it looks to be two dipoles fed separately. I assume that this is for spacial diversity.
Each dipole has an unusual feed in that the right hand side of the dipole is fed via a half-wave delay line. I presume that this is done to provide a good match and because it is so easy to do with PCBs. If you're not making a PCB antenna, then I wouldn't bother trying to mimic that system.
One important thing to keep in mind is that you need to decide if you want high gain with directionality, or low gain with (close to) isotropic coverage. In other words, some applications demand low gain in order to achieve (nearly) isotropic coverage.
If you're making a 'ground plane antenna' using the connector, then the four horizontal radials are typically about 5% longer than quarter lambda and can be bent slightly downward to increase the feed point impedance. The primary disadvantage of a ground plane antenna is the large volume (X, Y and Z) that it occupies.
A dipole can also be assembled onto a connector. Just a quarter lambda wire going each way. There's also the sleeve dipole where the feed goes into the far end of one element.
High gain antennas for 2.4GHz are well covered on the
cans for example, but there are better choices...).
Pay attention to polarity (H vs V). There can be a big (20-30dB) cross pol. loss if you not matched.
