Flowcharts used to be used when teaching programming in academia but this was years ago and nowadays that would be ridiculed.
They might be used for teaching garbage collection principles, reference counting and the like.
I find diagrams are useful for expressing data mappings and complex classification hierarchies (such as your example) but not algorithms nor control flow.
I am always suspicious of people who draw boxes around everything because it doesn't add any information to the diagram. Maybe little things such as a database symbol or something to represent a TCP port is acceptable. Most of the boxed diagrams I see can be better expressed with labels and arrows and this is good because it puts the perspective back onto I/O which usually ought to be your main concern.
Some of this might be overly general but I am totally with you on the circles issue. Totally.

So little time with serious hard core math to finish and ship results off to a machine shop that will use an old fashioned conventional Milling Machine - After the CMC does its job cause sometimes its what a machine is not designed to do vs a machine of old vintage that can still do stuff one does not need to do often enough to design the CMC to do it all -
LaBoot you said
> Flowcharts are useless for preparing to solve problems
Then you get bogged down in box's and symbols.
So sure I come from the old school way of doing it butttt I have taken lots of recent courses UCSD mostly engineering and some genetics stuff just to stay up to date and a couple of specialized math courses. Each one has text books with FLOW CHARTS in one place or the other
So put that all aside for the moment- This is what a Flow Chart can do for u LaBoot
You have a complex problem to solve - Your Girlfriend has a to do list - Get that tan in a booth then get nails done then get hair waxed off of puss then get that new bra she saw on tv then buy something to cook for you
To do list is step by step and can have a do loop in it cause maybe she did not make appoit for wax job and they were busy so she has to come back later
More complex problems can be put in box's circles etc and you see step by step what you need to consider and do next AND in PROGRAM MANAGEMENT - As I swing as I am about to swing down the halls of Qualcomm Campus - OUTSIDE the door is a Flowchart for all to see who are on a specific program so they can see how close everyone else is to solving the major program tasks AND IT MAKES THEM SAY OH SHIT I WILL BE THE Critical Path next not done if I don't get my ass in gear and grind the gears to get my shit done so I do not look like a fool in front of the rest of the team.
It also in program management lets people see much they no see cause they cannot attend every fucking meeting cause if they did they wood never get any work done which is about what I am going to do cause I do not want to be in that meeting in a few minutes cause I HAVE SO FUCKING MUCH WORK TO DO
Bottom line
I am currently doing one hell of a lot of math and without a flow chart I wood be Bat Shit Crazy - If you think flow charts are useless with stuff in a box as Anon B agrees?
Try doing some basic Matrix Math - In a box and lots of box's (Matrices) You might have a super complicated Calculus equation and other box's that look exactly the same 95% the same will have a Linear Equation and the next box will have a Non-Linear equation.
Trust this - Without a pattern to follow which can be called a flow chart - You are shit out of luck solving the problem unless you can get Math Labs to do it for you and if that is the case you end up as input device that one day will be replaced by Watson and u b on welfare
I LOVE FLOW Charts - I have reams of them on this project made by other people and they get paid a small fortune doing them and many have PhD n title - Good for buying a really really nice car and well
Out of here to meeting
Ritten in somewhat anger cause ONE PERSON is Critical Path fuck up on Flow chart output today and a whole fucking team of people are jammed up waiting for OUTPUT that Flow Chart said must happen three weeks ago and that one person has a small fight with her roommate and was in tears yesterday and NOW I HAVE TO agree to do that work for her to get her and team out of a jam and frankly its not the kind of work I should be doing - One more PERL Patch for C++ coming up cause I am good with PERL and suck at C++ grrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
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I heard they call them finite state automata diagrams nowadays.