alt Hacker NewsValue can only stabilise if there's either someone in charge adjusting the rate of printing to maintain a stable value. It cannot be done algorithmically as there's no way to determine the value from inside the system.
Non-deflationary currencies encourage hoarding which leads to wild swings in value. Deflationary currencies do much better. Look at the price chart of BTC vs XMR.
It depends how you measure value. By stabilise I mean stops growing in value by 50%/yr with big short term swings of 80%.
As it matures and gets close to it's ultimate value, volatility will naturally reduce.
Once it is used as the unit of account, everything else will fluctuate in value relative to bitcoin, which has more stable fundamentals than anything else on earth (fixed/zero issuance, liquidity etc), but this will be decades in the future when it's dollar value will be 8 or 9 figures in today's money