Then the light's gone over the fence to someone else's garden,
And the flowers stand there in the blue, keeping the colour to themselves

Last Light

I've been building a series of pages where the computer generates the pattern: tin-glazed tiles painted by rule, then cut tile and poured cement, heraldry, knotwork and, last time, a piece that breaks another piece. They've been travelling round Europe, borrowing from the art and the history of each place, and trying to capture something about how patterns repeat across the whole of the artistic world. These two are Andalusia again, Seville and Granada, and they sit at opposite ends of what a page can do with a pattern. Sebka paints nothing and lights everything. Fajalauza lights nothing and is all paint.

A wall of orange brick carrying a lattice of lobed arches that cross each other to make rows of scalloped lozenges, the openings sunk and in deep brown shadow, standing on rows of pale marble colonnettes, divided by brick pilasters and string courses with a row of studs, every edge throwing a long shadow to the left

The tarde preset. The Giralda's net at half past six in the evening, the sun low on the right and every lobe throwing a long tooth of shade.

One shape on a lozenge grid

The net on the upper storeys of the Giralda is called sebka, and it turns up on the Mudéjar towers of Teruel and Calatayud, on the Hassan tower in Rabat and the Kutubiyya in Marrakech. Lobed arches spring from a row of columns and go on crossing each other up the wall, so the face becomes a lattice of rhombi with every side scalloped.

It's the simplest rule I've written for any of these pages. Set out a lozenge grid. Take each lozenge, shrink it by the width of the band, scallop its sides inward with the number of lobes you've asked for, and cut it out of a brick face as an opening. The lattice is whatever brick is left between the holes. The bottom row are the same shape with their lower halves dropped down to the imposts, on jambs, so the net ends on a row of marble colonnettes the way the real ones do. Pilasters and string courses stand in front and divide the wall into panels. The geometry stops there, and everything else on the page is light.

Every shadow is cast

The face has three heights: the sunk openings and the fields of the arcade, the brick face itself, and the courses and pilasters standing proud of it. The sun is a direction. The wall faces south, the sun comes up on the left at six, stands highest at one and sets on the right at eight, and from its angle the page works out a slant: how far along the wall a point standing one unit proud throws its shadow.

Nothing on the page is drawn in shadow. Each level's shadow on the level below is that level's own outline, moved along the slant by the drop between them, with the caster cut back out of it. On an offscreen canvas that comes to a handful of compositing operations:

// the face onto the openings, one drop down pathAll(lg, sunk); lg.fill(); lg.globalCompositeOperation = 'destination-out'; pathAll(lg, mv(sunk, 1)); lg.fill(); // courses and pilasters onto the openings, two drops down lg.globalCompositeOperation = 'source-over'; lg.save(); pathAll(lg, sunk); lg.clip(); pathAll(lg, mv(proud, 2)); lg.fill();

Filling the opening and then punching out the same opening moved along the sun leaves a crescent on the side the light comes from, which is the shadow of the brick lip on the floor of the hole. A course standing two units proud throws its shadow twice as far into the openings below. The layer is laid over the wall with multiply, softened by a small blur so the edge isn't a knife cut, and made deeper the more squarely the sun strikes, without ever reaching black.

Three panels of the same brick lattice. On the left, morning light from the left throws long shadows to the right inside every opening. In the middle, at midday, each opening has only a thin rim of shade along its top. On the right, evening light from the right throws long shadows to the left

The giralda preset at half past seven, half past twelve and half past six. The geometry is identical in all three; only the sun has moved.

A shadow on a sunny wall isn't a darker version of the wall. It's the wall lit by the sky instead of the sun, so it goes blue, and it goes bluer when the sun is low and orange. The sun on the page has a colour of its own, near white at height and gold at the horizon, and the shade it leaves is the sky's. Multiplied over orange brick, that cool shade comes out as a deep brown with no warmth in it, which is what the openings of a brick tower look like against the lit face around them. At noon there's only a thin rim of it under the top of each opening.

Two smaller things do a lot of the work at a low sun. The mortar joints are struck back from the face, so each one fills with the shadow of the course above, and the brick suddenly reads as laid rather than printed. And the courses carry a frieze of studs, each one a low pyramid with four faces, so every stud has a face to the sun and a face away from it and the whole band glitters when the light rakes along it.

A brick wall with a wide lattice of two-lobed arches, each opening holding a glazed disc alternately green and white, the courses set with green and white glazed studs, morning light casting shadows to the right

The teruel preset. Aragón's Mudéjar towers set glazed discs in the openings and glazed studs in the courses, and they catch the sun differently from the brick around them.

There's an hour slider, and a time checkbox that runs the day. The presets are towers: giralda in the morning and again as tarde in the evening, teruel and calatayud in Aragón's brick with glazed discs or lime in the openings, hassan and kutubiyya in the stone of Rabat and Marrakech, and doncellas in Nasrid plaster after the Alcázar's courtyard. None of this went into the package. The shadow caster is three passes on offscreen canvases and it belongs to Sebka until another page wants it, which will probably be Rejería, wrought iron and its shadow on whitewash.

Fajalauza

Fajalauza is the pottery of Granada's Albaicín, named after the gate its workshops stood by. It's a cream tin glaze with copper green and cobalt blue laid on it thick and fast, and the same few things painted over and over: a pomegranate, the one on the city's arms; a plump bird with a raised tail; and a branch, running round the rim of a plate or across a row of tiles.

Fajalauza is a tile wall on the same engine as Jerez, with Granada's nouns. Nothing on it is lit. It's flat colour on a glaze, painted by the drifting brush every page in the engine shares.

A wall of cream tiles. At every other grout crossing four blue pomegranates point outward from a dark purple hub, with green leaves between them along the joints. At the crossings in between, a green ring of branch with small leaves surrounds a blue and green rosette

The granada preset. Four pomegranates meet nose out at every other crossing, a leaf along each joint between them, and the branch makes a wreath round the crossings in between.

The bird and the pomegranate are traced

I learned three times on these pages that a figure drawn from parts looks like a toy. A traditional figure that painters copied by hand for centuries has a shape the hand knows and a rule doesn't. So the pomegranate and the bird were traced from flat drawings from the start, the same way Delft's ships and Jerez's horse were.

The drawings come from an image model, on the terms the tracer wants: a pure white page, one solid gold fill for the body, a thick black line closing every part, red and blue for the parts that take another colour, and nothing else in the frame. The bird came back as a plump folk-art bird with a red wing scalloped in black, a blue fanned tail and a blue crest. The pomegranate came back split, with forty-five blue seeds packed in rows, a gold crown and two red leaves.

The tracer from the heraldry post classes every pixel by its nearest colour, walks the edges of each class into closed loops, simplifies them and normalises them to the figure's box. The bird is one silhouette, six loops of wing, seven of tail and crest, and twenty-one of ink. The pomegranate's seeds come through as forty-five separate loops, one per seed.

Two rows. In the top row, a flat drawing of a gold bird with a red scalloped wing, blue tail and crest, beside a wall of cream tiles each holding that bird in blue with a green wing and tail standing on a green sprig, blue and green flowers at the corners. In the bottom row, a flat drawing of a gold pomegranate split to show blue seeds, with two red leaves, beside the pomegranate tile wall in blue and green

The two drawings, and the walls traced from them. Gold became the main colour, red and blue the second, black the ink.

On the wall, gold becomes the main colour, washed thin and then again slightly off so it pools at one edge. Red and blue become the other colour, laid over a knock of glaze so they don't mix with the wash underneath. Black becomes the ink, laid last. The palettes carry a leaf and a seed colour beside the wash, so the two colours trade places from palette to palette: a blue bird with a green wing on the fajalauza palette, a green bird with a dark green wing on verde, and blue on white throughout on azul.

The pomegranate stands on the tile's diagonal, its stem at the corner and its crown pointing into the tile, so where four tiles meet, four pomegranates point outward from one hub. The bird stands in the middle of the tile, and each of the eight paintings a wall draws from turns it left or right on its own random stream, so a wall laid all one way up is a flock rather than one bird copied.

A wall of white tiles painted in cobalt only. Each tile holds a bird in a circle, standing on a sprig with a sprig either side, some facing left and some right, with a blue flower completed across every grout crossing

The alacena preset, all cobalt, every bird in its circle. Some face left and some face right, depending on how that painting came out.

The branch has to meet itself

The branch couldn't be traced, because it has to continue from one tile into the next however the wall is laid, mirrored, turned or every tile the same way up. A drawing can't promise that. A rule can.

Each stem is a quarter circle of radius one half round a corner of the tile. It reaches each edge at its midpoint and meets it square on, and every repeat the engine has maps edge midpoints onto edge midpoints, so the stem always arrives where the neighbouring tile's stem leaves. With a quarter circle round every corner, each grout crossing gets a whole ring, each ring touches its four neighbours at the midpoints of the tiles' edges, and the wall becomes one chain.

The first version put leaves on both sides of the stem, and the outward ones from four rings all crowded the middle of every tile into a dark knot. Now the leaves turn into the rings, each mirrored across the middle of its arc so the ring stays balanced, and the middle of the tile is left for three berries from each ring.

A wall of cream tiles covered by a continuous green branch forming a chain of touching rings, one ring round every grout crossing, with leaves turned inward and a small green and blue rosette in the centre of alternate rings

The rama preset on the verde palette. Every stem is a quarter circle of radius one half, so the rings close across the grout.

There are seven presets: granada, pájaro, rama, albaicín (an old yellowed cream with four pomegranates on every tile), alacena, carmen (the branch whole on every tile) and sacromonte (green birds under a manganese line). Fajalauza needed nothing from the engine beyond the variants option Delft added last time.

Simple at the rule

The two pieces have nothing in common in their code. Sebka's work is geometry and compositing, with no brush at all, and Fajalauza's is a palette, two traced figures and a quarter circle. What they share is that each one is simple at the rule and complicated where the material is. The lattice is a lozenge grid and the branch is a quarter circle, and nearly all the code on both pages goes on making brick sit in the sun and paint pool on a glaze.

The seventeen wallpaper groups are next: every way a pattern can repeat on a plane, as a control on the wall, in block-printed paper with the registration drifting.