Is there any sort of ram compression available for Tiger like RamDoubler in classic or ZRAM on Linux?
RAM Doubler took a portion of RAM and turned it into a RAM Disk, then applied a low level drive compression to the RAM Disk, and then deployed its own virtual memory system to that. In essence compressing memory.
I'm not aware of anything that exists on this front. I think it would be very difficult to build, and may be impossible to integrate into the OS.
The mechanism by which Classic Mac OS integrated this kind of thing is that RAMdoubler et al were entire replacement memory managers. It's almost certainly not possible to build something like that for OS X.
For better or worse, the fact that most 10.4-era PPC Macs in particular have relatively low RAM ceilings compared to 10.4's ability to eat RAM if you run a lot of software is Just Part Of The Charm Of The Era.
I don't remember if it was this thread or another but I was thinking the other day about how the late PPC and early Intel era is one of the few times it was possible, reasonable, and desirable to max out the RAM on a system up fairly early on in its life.
If memory compression had been possible, especially on PPC Macs with lower RAM ceilings but a potential couple more years of service life in them, I think it would have been built. This era had lots of new Mac users and 2006 was also the year laptops crossed over as the most popular type of computer in most contexts, so there was a strong presumptive market for software that could boost memory efficiency.
That said, based on my notes below about what RAM Doubler was actually doing, at least if TidBITS reported it correctly -- Mac OS X didn't have the specific shortcomings of the Classic Mac OS that made what RAMdoubler did necessary. In OS X, each application takes what it's using at the moment and no more. (The biggest exception to this is if Apple was doing disk caching in the RAM which would have been with a random available amount of RAM, Windows Vista did this a little too aggressive, Windows 10/11 still do but a bit less so and more for writes than prefetching things since random reads on SSDs have partly obviated the need for that.)
From this, it looks like it's more about compacting the existing RAM usage. It puts other applications into the area apps have allocated but aren't currently using. For example, in that blank area at the end of "Dreamweaver MX" in this screen shot.
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That can, of course, have changed over the years, but using a RAMdisk as the swap file destination seems like it would be an unnecessary limitation and an extra step in the process. It's likely that the final destination if things do actually use more RAM than you have is to the disk.