Kitchen Generator II
Kitchen Generator I ended with the appliances fixed and the casework as whatever the wall had left. That makes the cabinets sound like the easy part. They aren’t. Four appliances side by side, with no cabinet between them, have 4 × 3 × 2 × 1 = 24 possible orders, and Kitchen I’s two range rules throw out all but four of them: the range has to sit at one end with the sink beside it, and the fridge and dishwasher take the other two spots in either order, so 2 ends × 2 = 4. A cabinet goes the other way. Nothing throws anything out. So this one is me looking at the combinatorial explosion of cabinetry configurations — uppers and lowers with varying leaf counts and drawer arrangements. Every valid combination displayed at once.
How to read a card
A leaf is a door. An upper is the wall cabinet, a lower is the base cabinet, and a drawer row is one drawer in a stack on the lower. Each card in the drawing is one cabinet front in elevation, drawn at true scale: one scale across and up, the same for every card. The upper is a 30″ box hung from 54″ to 84″, split by its leaves. The lower sits on a 4″ toe kick under the 36″ top, with its drawer rows, 6″ each, across the top and its leaves below. Dashed lines on a leaf point to its hinges. The label over each row counts them: U for upper leaves, L for lower leaves, D for drawer rows. Under each card are its place in the list and its width.
What stays fixed
The heights. This generator doesn’t know how wide the cabinet is. Width is a separate catalog dimension, the 18–36″ in 3″ steps from Cabinets I, and a drawing at true scale needs one, so the exhibit draws each front at all seven widths, side by side in one row. Past that, nothing is fixed, and that’s the point: there are no rules here. Uppers, lowers and drawers vary independently, so the count is a straight product, upper choices × lower choices × drawer choices, where “no drawers” counts as a drawer choice.
What the list runs through
The list runs through the product in nested blocks. Two upper and two lower choices with no drawers: 2 × 2 × 1 = 4 fronts. Allow zero or one drawer row and it doubles to 8. Zero to two rows: 2 × 2 × 3 = 12. Three choices in each: 3 × 3 × 4 = 36. My original had sliders up to four leaves on each side and up to three drawer rows; read as ceilings, that’s 4 × 4 × 4 = 64 fronts for one cabinet at one width. The exhibit writes out all 64 at seven widths each, 448 drawings, and then starts again. The bar over the drawing marks where each block ends: drawings 28, 56, 84, 252 and 448.
What to notice
The count multiplies and nothing subtracts. Kitchen I was all subtraction: widths came out of a fixed wall and rules knocked out orders. Here every new choice multiplies every old one. Put Cabinets I’s seven widths under the 36 fronts and one cabinet position has 36 × 7 = 252 versions. Kitchen I’s opening example left 54″ of casework. There are seven ways to split 54″ into two widths from that family, 18 + 36 through 36 + 18, so two cabinets give 36 × 36 × 7 = 9,072 runs. That’s one short stretch of wall, before anybody picks a handle.
Look closely and the 448 drawings don’t read as 448 different things. Along a row, one front only gets wider, 3″ at a time; side by side, its 21″ and 24″ versions are hard to tell apart without the label. Down the list, one more drawer row moves the lower leaves down 6″. The enumerator counts every one of those as a new cabinet. A lot of what an enumerator counts as different, a person looking at it can’t tell apart.
Every valid combination
My original line says every valid combination. In this generator every combination is valid, because nothing here can be invalid without a width. Cabinets I already had the first real rule: door leaves max out at 24″ wide, 30″ for a more modern look. A 36″ lower with one leaf breaks it; the same front at 24″ is fine. The drawing marks those leaves in coral: 112 of the 448 drawings have one, or 56 against a 30″ limit. The generator keeps them all. The rule that prunes a cabinet front lives on width, and Kitchen II leaves width out. It can count the space. It can’t prune it yet.
The judgment
To a generator, the casework remainder isn’t slack. It’s where the explosion lives. The appliances are a small, rule-bound problem: 24 orders, four survivors. The cabinets are an open product with no rules until width shows up. So the hard part of a kitchen generator isn’t producing options; any loop can do that. It’s deciding which differences a person should ever see. A list of 448 fronts, most of them a 3″ step from the one beside it, is a catalog, not a design tool.