A fake bitcoin currency trader

Is this chart a mathematical trick? Yes, but we can pretend it is a banker bot currency trader, in red, betting against some 10 member banks, in blue, on the price of some currency relative to the bot virtual currency. Call that trade $/botcoin = p.  The traders make a bet in blue, and the bot immediately restores the flow constraint using the difference equation, p*p'-(1/2)p'' = 0. Bot coins are more valuable when the red line drops, and visa versa.

What is the trick?
I approximated the member banks, who bet, as a random draw about some range.  That is not true, member banks are going to bet around their current accounts.  Second, the betting is range bound so that the bot never has to lose dollars. The bot does a square root to make its bet, and when the radical in that root is negative, then means the bot has to make dollar losses from the past. Making up dollar losses is a shock, or an adiabatic change, it means the quant size for dollars has changed.  That is, the banker bot system has to scale up or down.

So this thing is not complete, it is me just learning how bot works. Much learning to do. The flow constraint means that dollars and bot coins can be sequentially ordered, they will be co-quantized within some uncertainty.  The banker bot should not really update the flow constrain until that ordering is threatened.  That ordering means the value 1 is constantly be computed by the system. But looking at the price, we see it always hovers about 1/2, and that tells me the system is being driven by the random draw with uses a constant variance. That variance in member banks bets will change as they adapt, and the bot should be holding off on its bets, it needs to undersample the member banks a bit, not necessarily make  the flow constraint at every bet.

Queue size:

The key number is the 1/2, that value should drop as more bets stack up in the queue. For example, the value of the dollar suddenly drops and member banks line up to dump dollars into their accounts. The bot should lower that number and make smaller adjustments per trade, thus spreading the bot coin gains among all the member banks. When no bets are in the queue, that means member banks know something that bot does not know, so bot wants to raise that number and get a bet or two to find out what's up. The bots value to any member bank is to have a good estimate about all the member banks activities.