# I Ching Algorithm: mutation

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Review binary sequence
`1010101000000111100100`
Applying The hexagram space theorem, we use convolution with the following parameters:
Len_in = 22; Len_Out = 6
len_w = 7; stride = 3
Filter = [1/7, 1/7, 1/7, 1/7, 1/7, 1/7, 1/7]
`‘101’010’1,00’0,00’0,11’1,100,100`
The six binary segments in the extracted window are
`1010101 0101000 1000000 0000111 0111100 1100100`
Output is a 6-element vector [4/7,  2/7,  1/7,  3/7,  4/7,  3/7]
Applying The theorem of problem space representation We get a 6-bit binary sequence
`100010`
We have two 3-bit subsequence
`100 010`
Upper hexagram is CHẤN, lower hexagram is ĐOÀI, the double hexagram is LÔI TRẠCH QUY MUỘI LÔI TRẠCH QUY MUỘI is a bad hexagram, the metal and wood are incompatible, the object hexagram harms the jubject hexagram, just enjoying the pleasure, it is difficult to develop.
Such an individual needs to be improved. We conduct chromosomal mutation.
In terms of hexagram space, it includes hexagrams and laws, and is "read only" to humans. I Ching transformation is a natural movement. Variable dime arises only from objective facts and not vice versa. Any operator of I Ching transformation is meaningless. Relying on the variable hexagram as a future hexagram to place events in the evolutionary route is impossible because then the qi of heaven and earth has moved. What we can do is process the data in the data space to catch new signals.
We do "I Ching transformation" the 6-bit binary sequence. Although the I Ching transformation is a normal transformation in nature, each dime of the hexagram turns from yin to yang or vice versa, but we transform the data therefore it is possible to change many dimes at the same time so it is called mutation.
We mutate the fourth bit, from 0 to 1
`100 010 -> 100 110`
get the hexagram LÔI THỦY GIẢI LÔI THỦY GIẢI is a good hexagram, the water-wood is mutual. This hexagram relieves tribulations and difficulties, opening a bright path for a new era.

Update Chromosomes
We rewrite the original chromosome and the resulting of convolution
`1010101000000111100100`
`‘101’010’1,00’0,00’0,11’1,100,100`
`1010101 0101000 1000000 0000111 0111100 1100100`
`100010`
The bit group corresponding to the fourth bit of a 6-bit binary sequence is `0000111`, it is converted bits 0 to 1, bit 1 to 0
`1111000`
It starts from the 10th gene to the 16th gene in the chromosome, we get new chromosome
`1010101001111000100100`
Because the updated 7-bit group interferes with neighboring groups, we can update the bits with a probability distribution function that focuses on the center and ignores the bits at the border.
`pi = (-(xi – 1)2 + 6 * (xi – 1)) / 9`
With the first bit x1 = 1, the update probability is
p1 = (-(1 – 1)2 + 6 * (1 – 1)) / 9 = 0
The same, similar,
p7 = (-(7 – 1)2 + 6 * (7 – 1)) / 9 = 0
Thus, the two outermost bits are not updated.
The remaining bits emphasize the center
p2 = (-(2 – 1)2 + 6 * (2 – 1)) / 9 = 0.6
p3 = (-(3 – 1)2 + 6 * (3 – 1)) / 9 = 0.9
p4 = (-(4 – 1)2 + 6 * (4 – 1)) / 9 = 1
p5 = (-(5 – 1)2 + 6 * (5 – 1)) / 9 = 0.9
p6 = (-(6 – 1)2 + 6 * (6 – 1)) / 9 = 0.6
The middle bit which be the fourth bit is always updated.

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