As bitcoin has blazed through the $3k range in about 1 week, the approach on $4,000 Bitcoins is now a reality.

Will $4,000 Bitcoins become a faint memory of Cheap Bitcoins also?

Its hard to know when then this rally will end.

Big time money managers are spending millions on bitcoins every day
Gold analysts are calling for Bitcoin to achieve 5% Gold MarketCap
(~$30,000 - $50,000 per coin)
Certain figures calling for $100,000 Bitcoins by 2020
$1 million per bitcoin

It's insanity, it's tulipmania!

But Bitcoins arn't tulips!

So where does it end?

-The Million Dollar Question!-

Since I have been involved in bitcoin and studied the charts, I have noticed a few similarities in the price movements since Bitcoin hit the exchanges many years ago.
(1 week interval of all-time pricing on Bitstamp)

(1 week interval look of previous pumps)

Here is the trend I have noticed on Bitcoin

When it pumps, it goes about 10x it's previous All Time High
Then it crashes
The price will get about 2x the previous All Time High as a low
Followed by a period where price stagnates
Then a small rally forms
Follow by a pump, repeating the process.

Chronologically:

$1 - $10 - $2 - $100 - $20 - $1000 - $200 - NOW?

This trend seems to work out fairly well if you study the graphs. What I also noticed is that the length of time it takes for the processes to occur is getting longer as is becoming apparent with the length of this recent 2 year long pumping period.

So based upon my research and expectations the next top can be expected at:

~ $10,000 per Bitcoin

Unfortunately, I would also expect a long period of declining prices lasting probably 5+ years where the price crashes down to ~$2,000, followed by a very lengthy pump to over $100,000 per coin.
If the time periods are getting exponentially longer for each cycle, then I would assume Bitcoin will be under $100,000 for at least another 50 years.
If this price correlation actually plays out

Bitcoin would become an excellent store of value for the next generation
(Following the next price decline, and expecting the next pump cycle to take 20+years to move each coin value $2,000 - $100,000)