I am going to connect them with the provided wires so I do not have to solder them together but it will be 1 long line like it was an 1800 LED strip
It seems that the colour patterns you want to use are extremely simple. So simple that a value could be computed for each LED with very limited memory usage.
The limitation of that is that it would require "on the fly" computation of the data stream. This would generally require more computational power than an ATmega328 running at 16 MHz, so you may need a faster processor, but then the faster processor would just as likely have more memory as well so you would not need the "on the fly" processing anyway.
What details would you like to know. I though I explain everything in the first post but by the sounds of it I missed something. Please let me know what you need.
He was able to run an 11 m strip using 3 power supplies capable of 10 amps each.
That's not really the point. The point is that Josh had over 1000 LEDs running without needing an Arduino with over 3000 bytes of ram. 1000 LEDs could need 60 amps, so Josh's PSU were not strictly adequate. But by keeping brightness low or by not lighting every led at once, he avoided overloading them. But that's not the clever thing he did. The clever thing was to do it with so little ram memory.
So then you have a power supply for each of six strips. If you chain them all together using the three pin JST connectors, you will necessarily be connecting all six separate power supplies in parallel. This also may be a problem as it is possible the supplies may interact. It would be better if you only chained the ground and data from one section to another - and this of course if you can resolve the memory requirement for 1800 LEDs as has been discussed so far.The limitation of that is that it would require "on the fly" computation of the data stream. This would generally require more computational power than an ATmega328 running at 16 MHz, so you may need a faster processor, but then the faster processor would just as likely have more memory as well so you would not need the "on the fly" processing anyway. And I have not even mentioned the need for the capacitors and series resistor.
I plan to only hook up jumpers for the data line
And the ground lines. Just don't connect the 5V lines between the PSU.For the caps, more is better . Ideally at least 1000uF per strip, close to where the power lines connect to the strip. They act as local "power reservoirs".For resistors, something around 330R~500R between the Arduino and the first strip, close to the strip. Will there be long distances between the strips? If so, they may also need resistors.
The PSU should already be grounded with the cord from the outlet to the PSU that I am using.
As for the Resistors, I plan to be a short as possible between strips without having to cut the wires and soldering. So I think the wires with the connector is about 3 inches long on each end so a total of about 6 inches between strips.
And as for the Capacitors, So you say to be as close to the strip as possible. With the two wires I am going to use, should I connect one end of the cap to 1 wire and the other end to the other wire or do both ends get connected to one wire? And instead of cutting to wires completely can I just slice the cover open and shove the cap in and heat shrink it closed?
That's the AC ground, its not the same thing. You must connect the DC grounds, between the Arduino and each/all strips.
You might get away without the resistors between the strips. If you don't use one, there is no risk of damage, its just that the signal may not be reliably received by the first led on the next strip. It will be easy enough to tell if that's happening, so hook them up temporarily, and if the data is not getting through, add more resistors.
The caps go accross the + and - wires. Caps of this size will be electrolyic type. You must connect them the right way around or they will probably explode. The cans are often marked with + symbol next to the positive terminal, but if not, there will be a white stripe next to the negative terminal.