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Generating Fractals with Postgres: Escape-Time Fractals

One not too well known aspect of SQL is that it’s Turing complete. This means any program you can write in a general purpose programming language, you can also write in SQL. In this post, I’ll show you how you can use some of the dark corners of SQL in order to generate fractals. We’ll ultimately wind up with a set of queries which will allow us to generate an entire class of fractals known as the “escape-time fractals”.

Common Table Expressions

Before we begin, I’m going to go over one very important SQL feature that I’m going to use a ton throughout this post. That feature is known as CTEs (common table expressions). CTEs effectively give you a way to define what are effectively variables in SQL. They are really nice for large SQL queries because they let you break down the query into smaller pieces.