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This introduction does not do LOGO justice but it's a start. LOGO is a programming language, pure and simple. There are two models that languages come in, compiled and interpreted.
What is a compiled language? In a compiled language the program is written and fed to a compiler. A compiler reads all your code and converts it to an executable form that your computer understands.
What is an interpreted language? An interpreted language does not get compiled; instead, as each line is read by the interpreter it executes it.
This is a slow process to execute (on the fly) like this, but has the advantage of not requiring a complete compile for each change. It's ideal in a learning environment. So have guessed what type of language LOGO is yet? Right, it's an interpreted language; at least this LOGO is anyway. LOGO also has another unique feature not offered in many other languages (none that I know of). That is, what's called 'Turtle Graphics'.
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What are turtle graphics? Turtle graphics is a simple and powerful set of commands to manipulate a turtle.