supply is a function of position. position, written e, is the total eth that has ever entered the curve, in wei. the function is
q(e) = K × ( 1 − S² / (S + e)² )
with K equal to 33 554 432 tokens and S equal to 512 eth. q is zero at zero, rises steeply, and bends toward K without touching it. the quantity S² over the square of S plus e is the fraction of K still unissued at position e; the curve issues the complement.
| position | supply | share of K |
|---|---|---|
| 0 eth | 0 | 0 |
| 212.077 eth | 16 777 216 | one half |
| 512 eth | 25 165 824 | three quarters |
| 1 536 eth | 31 457 280 | fifteen sixteenths |
| 3 584 eth | 33 030 144 | sixty three sixty fourths |
each doubling of S plus e cuts the remaining share by four. that is the whole shape: the curve is not exponential and does not decay by a fixed fraction per unit of eth; it decays by a fixed fraction per doubling of depth.