Sideways Through Time

We always travel forwards in time, and the idea of travelling backwards is out there. What about sideways though? If time were two dimensional and you could build a sideways time machine, what would it be like? If this were the case I like to imagine time as a kind of water drop along the glass wall of a shower. As the drop drips down the glass it creates a path behind it in the condensation which would be it's history, and the drop itself is the present. The gravity acting on to bring the drop lower and lower could be analogous to the entropy that drives time forward. Now, I build my machine, hop inside, and flip the switch. As the machine travels sideways my view from the inside would rapidly change from my present time in my universe, to the what the present looks like in the next nearest branch at my location, and so on as I continue further and further. Just like a time lapse video. I also like to think that perhaps as I stated earlier, the entropy would act as a gravitational force, drawing all time streams down. So to reach another time stream location exactly perpendicular to you, you would need to travel in a parabolic shape, like when playing catch with someone, and the further you travel away from your time stream, the more different things would become. In summary, As you travel sideways you travel to other temporal branches of your universe. The further away from your stream you travel, the more different things become. Depending on then location among the various streams you plan to travel to, you need to change your temporal angle to accommodate the entropic gravitation drawing all things toward the future. Finally, the fastest you can fall straight down temporally, is the speed of light (any faster and you would start crawling back up, since you would be going backward through time).