Until a whole country gets converted to a true capitalism, I would like to live in a sort of Galt's Gulch: a place where I do not have to pay any taxes and all property is private. In the book, the place was hidden with an science-fiction optical illusion screen. Is there a realistic way to do this today, to effectively hide an area?
Or, is there a pen way (legal way) to cloak a Galt's Gulch ? Note that any barter transaction between individuals is taxed.
Galt's Gulch in Atlas Shrugged is fictional concretization of "life as it might be and ought to be," and of the underlying principles that would make it possible and practical. The course of action which those principles imply is to speak out in support of those principles and in opposition to their opposite, in order to aid the progress of Objectivist principles. Another way to help the spread of Objectivism is to contribute financially to organizations like The Ayn Rand Institute that are engaging in such intellectual advocacy. It is only if speech has been prohibited through government censorship (as depicted in Atlas Shrugged, for example) that it becomes rationally appropriate to withdraw from the world as it collapses.
Is there a realistic way to do this today, to effectively hide an area [using advanced technology]?
Not that I know of. There simply are no shortcuts. To build Atlantis, one must work for it. One must work to spread the right philosophy.
Or, is there a pen way (legal way) to cloak a Galt's Gulch ?
This formulation doesn't make sense. What is "a pen way (legal way)"? Cloaking an area seems to refer to a technological way. "Pen way" would seem to refer to intellectual advocacy, but how would that "cloak" anything literally, not just figuratively? In real life, one will not achieve a value like Galt's Gulch if one starts out by giving up.
If "cloak" actually is intended to mean hiding the true nature of something in plain sight, but keeping it unnamed and intellectually undefended, it would be a self-destructive course of misrepresentation and deception, constantly leaving one in fear of exposure and vulnerable to public condemnation upon being exposed as a fraud for pretending to be something that one isn't. Note that even in the controlled, censored society in Atlas Shrugged, Galt spoke out very publicly as soon as he had a suitable opportunity. So did America's founders in our Declaration of Independence.
This question has actually been asked countless times by many readers of Ayn Rand's works, although I couldn't find a previous instance on this particular website. The fact that Galt's Gulch has such strong appeal to rational readers is a testament to the power of Ayn Rand's writing and the fundamental philosophy from which she wrote.
Update: Establishing Capitalism
In a comment, the questioner asks:
Do you think if we get enough people we could annex some territory from USA (or some existing country) and set it up as capitalism?
That's not exactly what Galt's Gulch in Atlas Shrugged was, and certainly not how it was created. The story of how it was created is presented in detail in Part III Chapter I, which spans pp. 652-699 in my Signet paperback edition of Atlas Shrugged. On page 694, Dagny is hearing from all the major strikers about how they decided to join the strike, and how they eventually established vacation residences (or full-time homes) in Galt's Gulch. Dagny asks Midas Mulligan the following question, and he explains the background to her:
"It was you who established this valley?"
This is followed by discussion of quitting one's profession but continuing to pursue it secretly; meeting other strikers occasionally; eventually becoming able to vacation in Galt's Gulch for a full month out of each year; each striker building his own house in the Valley; and eventually most of the residents becoming able to live there full time. On p. 695, Mulligan reinterates:
"We are not a state here, not a society of any kind—we're just a voluntary association of men held together by nothing but every man's self-interest. I own the valley and I sell the land to the others, when they want it...."
On p. 697, Dagny says to Galt:
"What do they call this place," she asked.
Note that Galt's Gulch was never intended as an alternative "capitalist" society. It was just a vacation retreat, where strikers could come for some temporary relief from the collapsing society around them on the outside. The ability of so many of the strikers eventually to live there full time came much later, and was intended to last only until the moral code of the looters collapsed and opened the way for the strikers (or their descendants, if the strike outlasted the strikers) to return.
The exact story of the Valley in Atlas Shrugged really ought to be studied in far greater depth by those who are quick to dream of fleeing to an alternative, parallel society while the existing, corrupt one and especially its moral code still exist and have any lingering appeal to the general public.