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simultaneously—” I touched the orange circle to stop the animation, copied its attributes, pasted them onto the green circle, and restarted the animation. “The orange and green circles expand, and eventually they have to overlap, right?”
    Kurokawa watched intently. The red pencil he’d been toying with had migrated to a perch behind one ear. That was the first time I’d ever seen someone do that with an AR widget. Zucca …
    “That’s how you draw a straight line.”
    “Just a second, Mamoru. Where is the line drawn?”
    “Between the towers. Let’s slow down the animation and mark the intersections of the circles.”
    I adjusted the controller to slow down the animation. The two circles kept expanding and finally touched at the midpoint.
    “The messenger pulses join midway between the towers. The plants in this location receive both messengers at the same time. That activates the genes for color expression.”
    I stopped the animation and drew a red x where the circles touched. Kurokawa nodded. Now he had the pencil wedged between his nose and upper lip.
    I restarted the animation, and the circles began to overlap. “When the messengers are released simultaneously, color genes are activated in plants that are the same distance from both towers. As the crops change color, they draw a line right down the middle of the space.”
    I ran the animation four times, adding four more marks above and below the first mark where the edges of the overlapping circles touched. Now I had nine marks lined up vertically between the towers.
    “Short pulses produce narrow lines. Longer pulses—several seconds, say—produce thicker lines. In this case, two circles have drawn a single line.”
    “I see. So it’s as much about controlling the environment as controlling the genetics. But …”
    Kurokawa was rolling the pencil between his palms, head cocked to one side. I knew how he felt. The first time I heard this explanation, I couldn’t figure out how gene mappers made the jump from straight lines to the complicated figures being produced in the real world.
    “Bear with me a bit more, Takashi. If we want a curved line, we just delay one of the messengers.”
    I reset the animation, this time with the green circle starting later. The orange circle moved outward to contact the green circle a bit closer to its tower. I used the blue marker to mark the contact points. Now the plot was a curve.
    Kurokawa leaned forward and started helping me, adding marks to the plot here and there, more or less at random, but accurately. He was getting the hang of it.
    “All right, I understand. With only two towers, you can draw straight lines of different widths or curved lines.”
    “Right. Say you add another orange tower to form an equilateral triangle. Release the messengers at the same time and you can draw right angles. Vary the timing and you can trace a variety of curved lines.”
    I got to work adding more towers and circles. Soon the table was covered with overlapping waves tracing complicated patterns. Both of us were busy adding marks to the intersection points when Kurokawa said, “So far so good. I think I grasp the principle. But can you really use this to draw a logo? The towers are fixed, and the terrain is uneven. I still don’t see how you could draw complicated figures like logos and letters.”
    “What I do first is build a kernel of the design with a few towers. I guess it’s easier if I show you.”
    I opened my workspace and pulled a preliminary sketch from the Mother Mekong project file. Zucca’s stage rendered it as an old-style blueprint. The layout showed fifty or so towers surrounding the letters L&B depicted in spidery lines. The design was far from a logo—all I had at this point was the size of the design and the rendering topology. For L&B, L had no enclosed space, while & and B each had two enclosed spaces.
    “The mapper has to specify the initial layout manually. First I create a sketch like