Here is the TrueBasic program that generated the images of seed packing.

! seed packing LET s = 400 ! set window size - large to make room for type SET WINDOW 0,s,0,s LET g = .5*(5^(.5)+1) ! set spacing factor !LET g = sqr(2) !Let g = pi !Let g = 7/31 LET n = 80 ! set number of seeds LET a = 30 ! set size of (eqil triang) seed LET i = 1 ! initialize LET m = a/2 DIM h(200) ! NOTE this must be at least n DO while i < n+1 LET x = (i*g - int(i*g)) * s !calculate ith x-coordinate LET gim = x - m IF gim < 0 THEN ! fix to be mod s LET gim = gim + s END IF LET gip = x + m IF gip > s THEN ! fix to be mod s LET gip = gip - s END IF LET h(i) = m*sqr(3) !h(i) will be height of APEX LET j = 1 DO while j < i LET xj = (j*g - int(j*g)) * s LET gjm = xj - m IF gjm < 0 THEN LET gjm = gjm + s ! fix to be mod s END IF LET gjp = xj + m IF gjp > s THEN ! fix to be mod s LET gjp = gjp - s END IF CALL hij( gim, gip, gjm, gjp) IF hnew > h(i) THEN LET h(i) = hnew END IF LET j = j + 1 LOOP CALL tri ( x, h(i)) LET i = i + 1 Pause .1 LOOP SUB hij(gim, gip, gjm, gjp) !correction to height i to miss triangle j CALL dif (gip, gjm) !determine overlap between base of IF d < 0 THEN !i-th triangle and base of j-th LET hnew = m*sqr(3) EXIT SUB END IF CALL dif (gip, gjm + m) IF d < 0 THEN LET hnew = h(j) + sqr(3)*(gip-gjm) EXIT SUB END IF CALL dif (gip, gjp) IF d < 0 THEN LET hnew = h(j) + m*sqr(3) EXIT SUB END IF CALL DIF (gim, gjm + m) IF d < 0 THEN LET hnew = h(j) + m*sqr(3) EXIT SUB END IF CALL DIF (gim,gjp) IF d < 0 THEN LET hnew = h(j) - sqr(3)*(gim-gjp) EXIT SUB END IF LET hnew = m*sqr(3) END SUB SUB dif (a, b) !calculate distances mod s LET d = a - b IF d < -s/2 THEN LET d = d + s EXIT SUB END IF IF d > s/2 THEN LET d = d - s EXIT SUB END IF END SUB SUB tri (a,b) !draw triangle and plot i inside PLOT a-m,b-m*sqr(3);a,b PLOT a,b;a+m,b-m*sqr(3) PLOT a-m,b-m*sqr(3); a+m,b-m*sqr(3) PLOT TEXT, at a-8,b-m*sqr(3)+2: str$(i) END SUB GET key zz END

Back to previous irrational page.

Back to first irrational page.

*Comments: webmaster@ams.org
© copyright 1999, American Mathematical Society.*