Definition:Pea Pattern/Ascending/Examples
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Examples of Ascending Pea Pattern
Ascending Pea Pattern on $111$
| \(\ds \) | \(\) | \(\ds 111\) | ||||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 31\) | three $1$s | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 1113\) | one $1$, one $3$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 3113\) | three $1$s, one $3$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 2123\) | two $1$s, two $3$s | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 112213\) | one $1$, two $2$s, one $3$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 312213\) | three $1$s, two $2$s, one $3$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 212223\) | two $1$s, two $2$s, two $3$s | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 114213\) | one $1$, four $2$s, one $3$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 31121314\) | three $1$s, one $2$, one $3$, one $4$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 41122314\) | four $1$s, one $2$, two $3$s, one $4$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 31221324\) | three $1$s, two $2$s, one $3$, two $4$s | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 21322314\) | two $1$s, three $2$s, two $3$s, one $4$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 21322314\) | two $1$s, three $2$s, two $3$s, one $4$ |
and a fixed point has been reached.
Ascending Pea Pattern on $231$
| \(\ds \) | \(\) | \(\ds 231\) | ||||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 111213\) | one $1$, one $2$, one $3$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 411213\) | four $1$s, one $2$, one $3$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 31121314\) | three $1$s, one $2$, one $3$, one $4$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 41122314\) | four $1$s, one $2$, two $3$s, one $4$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 31221324\) | three $1$s, two $2$s, one $3$, two $4$s | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 21322314\) | two $1$s, three $2$s, two $3$s, one $4$ | |||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 21322314\) | two $1$s, three $2$s, two $3$s, one $4$ |
and a fixed point has been reached.
Ascending Pea Pattern on $10,213,223$
| \(\ds \) | \(\) | \(\ds 10213223\) | ||||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 10213223\) | one $0$, two $1$s, three $2$s, two $3$s |
and so is seen to be a fixed point.
Ascending Pea Pattern on $1,031,223,314$
| \(\ds \) | \(\) | \(\ds 1031223314\) | ||||||||||||
| \(\ds \) | \(\leadsto\) | \(\ds 1031223314\) | one $0$, three $1$s, two $2$s, three $3$s, one $4$ |
and so is seen to be a fixed point.