So there's a companion PDF to How to Design Programs (HtDP) called How to Design Worlds (HtDW). And I'm wondering how much of HtDP do I have to read/know to be able to start reading HtDW? Are the chapters from the two books correlated in any way?
How does HtDW correlate with HtDP?
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If you're reading the second edition of HtDP, then part 2 (Fixed-Size Data) already incorporates a lot of material that you need to know for designing worlds. In any case, after you have read about structures in either HtDP text (define-struct, etc.), that is probably an appropriate time to look at HtDW if you would like, because you need at least structures to make animations that are more than just trivial.
Try reading Chapters 1-4 of HtDP 2e
HtDW is meant to be a companion to HTDP, in the sense that the early stuff in it doesn't require much at all (The prologue, Chapter 1, of HtDP 2e), since it's just limited to basic arithmetic and images. But other material in it depends on design programs that work with arbitrarily-long list data, and that's Chapter 4.