Comment by drostie

Just to answer your question with regards to (2):

Suppose I open up LibreOffice Calc, and my first row gets the values "c", "x", "y" in that order, as labels for three columns. The second row gets the values 2, -2, 0. The third row gets the odd formulas:

    =A2, =B2 + 0.02, =B3 * B3 + A3 * B3 - 1

Now I highlight C3 and drag it up to C2 (the y=0 term which shouldn't be y=0 is now correct). I also highlight A3 through C3 and drag it down, until my x's range from -2 to +2; this happens at row 202.

The key thing is, this "dragging autofill" has quickly managed to make all of the y computations dependent on the same c, whose authoritative value is stored at cell A2. (I can also change what x's I look at by tweaking the cell B2.)

So I highlight the x and y columns, click the Chart button, to do a scatterplot, lines only -- no point markers. Then I need to kill the autoadjustment of the y axis because it will confuse me, so I set it to go from y = -5 to +10.

Now I can just start modifying this parameter c in cell A2, and see how the graph changes. I might notice for example that the vertex of the parabola hits a maximum when c = 0. That's an interesting feature; it suggests that the vertex of the parabola describes its own parabola as you vary c. Et cetera.

The only reason for doing it this way is because that is the easiest way I know of to get the computation right for 200 data cells. You're right, I could hand-write 200 different computations to all point to A2. It would take a long time and I would hate my life. I could also write in the value "2" and whenever I want to change it, drag across 200 rows. But then I would never get to see how this thing changes. (If you've never seen it, see Bret Victor's "Inventing on Principle" talk for a discussion of the power of having a direct connection with your artistic creations.)