General Report on Tunny

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22B Page 47

In order to prevent simple statistical recognition of the chi-stream each individual chi pattern is constructed with

(1) As nearly as possible an equal number of dots and crosses in the undifferenced and differenced wheel.

(2) No stretch of 5 or more identical consecutive characters in the undifferenced wheel. (See R5 p 4.)

Alleged chi patterns fulfilling these conditions are said to be 'legal'.

The conditions of legality are most obviously fulfilled by the pattern:

Χ:

.

.

x

x

.

.

x

x

.

.

ΔΧ:

.

x

.

x

.

x

.

x

.

x

A few of the patterns recovered consisted entirely of this pattern and were known as 'perfect wheels', e.g.

Χ5:

.

.

x

x

.

.

x

x

.

.

x

x

.

.

x

x

.

.

x

x

.

.

x

ΔΧ5:

.

x

.

x

.

x

.

x

.

x

.

x

.

x

.

x

.

x

.

x

.

x

x

In other cases the pattern was used over shorter stretches.

In the construction of chi patterns no attention was paid to the distribution of dots and crosses in the Δ² wheel. However, empirical evidence (see R3 p. 18) shows that                                                                                                B1

The fact that Δ²Χ_i → x can be seen to be a natural result of the conditions of legality and the popularity of the pattern . . x x . . x x

The following table gives the conditions of legality in numerical terms:

Wheel	Length	No. of crosses in Χ	No. of crosses in ΔΧ	Av. no. of crosses in Δ2Χ
1 2 3 4 5	41 31 29 26 23	20 or 21 15 or 16 14 or 15 13 11 or 12	20 16 14 12 or 14 12	26 19½ 19 16½ 14

Fig. 22(I)

The number of legal chis is discussed in 25X, and the frequency of various patterns of 5 and 10 consecutive characters in R3 pp. 125, 126.

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