Dicksonia antarctica Tasmanian tree fern

Dicksonia antarctica frond as rendered by code. From Trees of Stanford and Environs, Ronald Bracewell

A rather surprising tree from cool, moist gullies, which is planted in shady out-of-the-way locations, for example at the north side of the Faculty Club. The fronds may be up to 6 feet long and a yard wide; when dead they are cut back to stubs and give the trunk a characteristic appearance. The pinnae bear pinnules and they in turn are further dissected. See Sphaeropteris for the other kind of tree fern on campus. Both kinds may be found in the enclosed southwest courtyard of Jack McDonald Hall.

How does nature pack the complexity of a tree into a tiny seed? I tried to instruct a mechanical printer to compose a fern leaf, dot by dot, consciously aiming to specify the fewest leaf dimensions and briefest set of instructions for using those data. The illustration of the computed leaf shows how rich a pattern can be specified in detail by the few lines of BASIC below. A lengthy description of the leaf in English can be imagined, and botanists do indeed attempt to unambiguously describe leaves using an extensive technical vocabulary. Nature presumably records the program for an ideal leaf in DNA symbols, though the encoded ideal is often frustrated by a variety of hazards arising during growth.

FOR I=0 TO 4; READ A(I),B(I),C(I),D(I),E(I),F(I); NEXT I
X=0; Y=0
FOR I=1 TO 30000
R=RND; K=(R>0.01)+(R>0.08)+(R>0.85); Tmp =A(K)*X+B(K)*Y+C(K)
Y=D(K)*X+E(K)*Y+F(K)
X=Tmp; U=1760*X; V=44700*Y DIV 28; PLOT(U,V)
NEXT I
DATA 0,0,0,0,0.16,0,0, 0.2,-0.26,0.23,0.22,0,0.2
DATA -0.15,0.28,0.26,0.24,0,0.2, 0.85,0.04,-0.04,0.85,0,0.2