By A.E.R. Woodcock

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0 B : - I . 0 D : - 2 . 0 B = - I . O Fig. 0 B = - I . ed Surface Projections of Wigwam Sections of the Star 8 Catastrophe V = ~ on the p l ~ e Ax 6 Bx 5 + --~- + -~-- Cx 4 Dx 3 + -~- + -~-+ Ex 2 -~- + Fx. (D,E) A negative, B and F zero and C running from +20 to zero (Fig. 34) produces a series of sections typical of the Wigwam Catastrophe for example Fig. 13). (See, As before, it is possible to elucidate the structure of the cuspoids by unfolding along a moving slice of the higher order catastrophes.

0 E=+<0 Fig. 0 Fig. 0 E:+l. 0 E:+I. 0 E=-I,0 Fig. 0 B : 0 . 0 41 Ruled Surface Projections of the Star Catastrophe 8 V = ~ Ax 6 Bx 5 Cx 4 Dx 3 Ex 2 + --~-- + -~-- + --~- + --~- + --~- + Fx. onto the ~lane (E,F) When A is negative, C large and positive and B and D zero, the singularity is simply cuspoid (Fig. 24, 25 and 26). However, as C is reduced, two Swallowtails begin to develop one on either edge of the cusp (see, for example, Fig. 24, C = +35 and +30); as C is further reduced than these Swallowtails grow to dominate the picture with the initially larger cusp region decaying to insignificance.

0 E:+l. 0 E:+I. 0 E=-I,0 Fig. 0 B : 0 . 0 41 Ruled Surface Projections of the Star Catastrophe 8 V = ~ Ax 6 Bx 5 Cx 4 Dx 3 Ex 2 + --~-- + -~-- + --~- + --~- + --~- + Fx. onto the ~lane (E,F) When A is negative, C large and positive and B and D zero, the singularity is simply cuspoid (Fig. 24, 25 and 26). However, as C is reduced, two Swallowtails begin to develop one on either edge of the cusp (see, for example, Fig. 24, C = +35 and +30); as C is further reduced than these Swallowtails grow to dominate the picture with the initially larger cusp region decaying to insignificance.