<p> Stem(data) </p>

d29e20af-7dde-4318-9177-6b2f19911b92 14 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

Stem construction over a data set data Stem stemX 1 data rows range : i 1 stemX rows range stem i el data i 1 el data i 2 el data i 1 el 022 mat : for i 1 stem rows 1 - range stem i el stem i el stem i 1 + (1 el 1 el 012 mat stack : for V stem 1 el : j 2 stem rows 1 - range V V stem j el stack : for V V data data rows row stack : 71 line :

The Hofstadter sequemce

n 1000 :

i 1 n range Q i el 1 i 1 ≡ 1 i 2 ≡ Q i Q i 1 - el - el Q i Q i 2 - el - el + cases : for

idx 1 n range :

Hof idx Q augment :

X Hof 1 col : Y Hof 2 col : 12 mat

X Y Slope X Y Intercept 21 mat 0.5021 2.3351 21 mat

Hof 2.335 0.5 x * + 2 1 sys

c X Y Intercept :

i 1 n range h i el Q i el i 2 / - c - : for

Detrend idx h augment :

Burst: [24, 48, 96, 384, 776]

Detrend 0 2 1 sys

About this sequence, Steven Finch [Mathsoft] had a longer discours but no application. As Steven observed, slope is apparently asympotic 0.5, but Intercept is vagary. That may simply mean Intercept is in some ways inappropriate, suffering from the weight of the bursts. Silently it may affect projects of similar nature.

The Hofstadter sequemce

j 400 :

i 1 j range Ω i el 1 i 1 ≡ 1 i 2 ≡ Ω i Ω i 1 - el - el Ω i Ω i 2 - el - el + cases : for

idx 1 j range :

hof idx Ω augment :

vx hof 1 col : vy hof 2 col : 12 mat

vx vy Slope vx vy Intercept 21 mat 0.5046 1.8938 21 mat

hof 0 0.5 x * + 2 1 sys

c vx vy Intercept :

i 1 j range λ i el Ω i el i 2 / - 2 - : for

Detrend idx λ augment :

Burst: [24, 48, 96, 192, 384, 776] ... distinctive burst appear & 96 as they can be detected

Detrend Stem 24 16 24 16 - 2 2 mat 48 16 48 16 - 2 2 mat 96 40 96 40 - 2 2 mat 192 40 192 40 - 2 2 mat 6 1 sys

The Hofstadter sequemce

j 6208 :

31042 * 6208

i 1 j range Ω i el 1 i 1 ≡ 1 i 2 ≡ Ω i Ω i 1 - el - el Ω i Ω i 2 - el - el + cases : for

idx 1 j range :

hof idx Ω augment :

9619238477615523104620817 mat

hof 1 0.5 x * + 2 1 sys

hof hof 31046208 range 12 range el :

vx hof 1 col : vy hof 2 col : 12 mat

vx vy Slope vx vy Intercept 21 mat 0.5003 2.7635 21 mat

Conclusion . . .

1. slope is close true 0.5 2. intercept uncertain

]]>

0.4995 0.5003 21 mat Mean 0.4999

0.5134 1.1782 21 mat 0.509 0.7837 21 mat 0.5027 2.0114 21 mat 0.5008 3.139 21 mat 0.4995 5.3764 21 mat 0.5003 2.7635 21 mat 16 mat