Power Law:(13)Tendency to LN(A) - LN(B)

(2008/10/30-2008/11/01)

LN(A) - LN(B)の傾向を探る。
It searches for the tendency to LN(A) - LN(B).

~~~
[0]プロット方針,Policy to plot
以前やっていた以下の方法は止める。意味がないため。
The following methods are stopped. Because it is not significant.

A)Power Law:(6)で、A>1のB値の変換。ポイントを線で結ぶ。
A)In Power Law:(6), B value of A>1 is converted. The point is connected in the line.

B)Power Law:(5)で、ポイントを線で結ぶ。
B)In Power Law:(5), The point is connected in the line.

~~~
[1]
Power Law:(11)の段階でのデータをプロットする。
Data at the stage of Power Law:(11) is plotted.

powerlaw-11-a-b.txt
===
"A","B","memo","Category"
-3.21,104660,"Power Law:(5),p.182,Fig.5-39(a)",Industry?
-2.457,4102.56,"Power Law:(5),p.182,Fig.5-39(b)",Industry?
-2.416,5.95e3,"Power Law:(5),p.182,Fig.5-39(c)",Industry?
-1.246,74,"Power Law:(5),p.128,Fig.4-14",Nature
-1.1818,5.337e4,"Power Law:(5),p.111,Fig.4-3",Electric
-1.092,24.926,"Power Law:(5),p.61,Fig.2-16(2)",Nature
-1.035,63.065,"Power Law:(5),p.123,Fig.4-10",Electric
-1.013,17.635,"Power Law:(5),p.63,Fig.2-18",Economy...human activity
-1.0123,20.75,"Power Law:(5),p.60,Fig.2-15",Economy...human activity
-1,1e4,"Power Law:(5),p.62,Fig.2-17",Culture?...human activity
-1.0,5.62e3,"Power Law:(5),p.175,Fig.5-33",Bio
-1,100,"Power Law:(5),p.125,Fig.4-12",Nature
-0.991,18.52,"Power Law:(5),p.61,Fig.2-16(1)",Nature
-0.767,200,"Power Law:(5),p.108,Fig.4-1",Electric
-0.353,58.214,"Power Law:(4),table.1",Bio
-0.29758,15.5,"Power Law:(3),p.242,Fig.44",Bio
-0.249,31.174,"Power Law:(7),p.27,Fig.3-1",Bio
-0.249,159.9,"Power Law:(7),p.36,Fig.3-2",Bio
-0.249,212.878,"Power Law:(7),p.36,Fig.3-2",Bio
-0.74,23.2,"Power Law:(8),p.22,Fig.2",Bio
-0.518,390,"Power Law:(8),p.24,Fig.3",Bio
-0.692,6.971e3,"Power Law:(8),p.26,Fig.4",Bio
-2.154,3162,"Power Law:(9),p.129,Fig.9",web...human activity
-6.179,1.234e5,"Power Law:(10),p.37,table",Nature...human
-2.1,1e6,"Power Law:(11),Fig.1",web...human activity
===

data_ab <- read.csv("powerlaw-11-a-b.txt");
> data_ab
A B memo Category
1 -3.21000 104660.000 Power Law:(5),p.182,Fig.5-39(a) Industry?
2 -2.45700 4102.560 Power Law:(5),p.182,Fig.5-39(b) Industry?
3 -2.41600 5950.000 Power Law:(5),p.182,Fig.5-39(c) Industry?
4 -1.24600 74.000 Power Law:(5),p.128,Fig.4-14 Nature
5 -1.18180 53370.000 Power Law:(5),p.111,Fig.4-3 Electric
6 -1.09200 24.926 Power Law:(5),p.61,Fig.2-16(2) Nature
7 -1.03500 63.065 Power Law:(5),p.123,Fig.4-10 Electric
8 -1.01300 17.635 Power Law:(5),p.63,Fig.2-18 Economy...human activity
9 -1.01230 20.750 Power Law:(5),p.60,Fig.2-15 Economy...human activity
10 -1.00000 10000.000 Power Law:(5),p.62,Fig.2-17 Culture?...human activity
11 -1.00000 5620.000 Power Law:(5),p.175,Fig.5-33 Bio
12 -1.00000 100.000 Power Law:(5),p.125,Fig.4-12 Nature
13 -0.99100 18.520 Power Law:(5),p.61,Fig.2-16(1) Nature
14 -0.76700 200.000 Power Law:(5),p.108,Fig.4-1 Electric
15 -0.35300 58.214 Power Law:(4),table.1 Bio
16 -0.29758 15.500 Power Law:(3),p.242,Fig.44 Bio
17 -0.24900 31.174 Power Law:(7),p.27,Fig.3-1 Bio
18 -0.24900 159.900 Power Law:(7),p.36,Fig.3-2 Bio
19 -0.24900 212.878 Power Law:(7),p.36,Fig.3-2 Bio
20 -0.74000 23.200 Power Law:(8),p.22,Fig.2 Bio
21 -0.51800 390.000 Power Law:(8),p.24,Fig.3 Bio
22 -0.69200 6971.000 Power Law:(8),p.26,Fig.4 Bio
23 -2.15400 3162.000 Power Law:(9),p.129,Fig.9 web...human activity
24 -6.17900 123400.000 Power Law:(10),p.37,table Nature...human
25 -2.10000 1000000.000 Power Law:(11),Fig.1 web...human activity
>

~~~
[1-1]log10で出力,output by the common logarithm.
>plot(abs(data_ab$A), data_ab$B, log="xy")

タイトル、ラベルをセット。
The title and the label are set.

>plot(abs(data_ab$A), data_ab$B, log="xy", xlab="log10(abs(a))", ylab="log10(b)", main="Scatter chart:a-b, Power Law(11)")

~~~
[1-2]log,LNで出力,output by Napierian logarithm.

>plot(log(abs(data_ab$A)), log(data_ab$B), xlab="log(abs(a))", ylab="log(b)", main="Scatter chart:a-b, Power Law(11)")

垂直線を引く。何があると予想している。
The perpendicular line is pulled. It is expected that it is what.
>abline(v = log(1), col="red")

水平線を引く。これにはあまり意味がない？特定値に収束していると期待していたが。たとえば、LN(900)とか。
The horizon is pulled. Isn't it so significant to this?Though it was expected
that it settled to a specific value. For instance, LN(900).
>abline(h = log(1000), col="red")
>abline(h = log(800), col="red")

~~~
[2]
何かが見えるか？
Do you see anything?

Power Law:(7)から、Power Law:(11)までのデータで、パターンを模索していた。
It groped for the pattern by data from Power Law:(7) to Power Law:(11).

可能性として、以下を検討した。
The following were examined as a possibility.

[2-1]20081030-2205-,案1,Idea 1

A)A=1.0の近傍の縦方向は、共鳴エリア？すべてのBを許容する。
A)Is the vertical direction near A=1.0 a resonance area? All B is allowed.

B)左下から右上斜め方向にクロスで、プロットが収まる。
B)The plot is installed from the left under in crossing for on the right diagonal.


[2-2]20081031-0715-,案2,Idea 2
：案１のlog10をlogにした。Log10 of idea 1 was made log.

A)A=0で、クロス？
A)It crosses by A=0?

B)左下から右上斜め方向にベルト的に、プロットが分布？
B)Is the plot distributed from the left under belting it for on the right diagonal?


[2-3]20081031-0937-,案3,Idea 3
：プロットデータを追加。The plot data is added.

A)A=0で、クロス？
A)It crosses by A=0?


[2-4]20081101-0843-,案4,Idea 4
：プロットデータを追加。The plot data is added.

B)左下から右上斜め方向にベルト的に、プロットが分布？
B)Is the plot distributed from the left under belting it for on the right diagonal?

いたずら書きあり。Mischief writing.
~~~
end

Power Law:(12)Graph,LN-LN in R

(2008/10/30)
Rで両対数グラフを出力する。
Both logarithm graph is output by R.
~~~
[1]例：Rの動作確認用
[1]Example:To confirm the operation of R
http://www.yukun.info/blog/2008/09/r-read-csv-file.html

読み込むCSVファイルは2007年度のセリーグの打撃成績の順位です。
The read CSV file is an order of the batting result of Central League in fiscal year 2007.

参考：2007年度 セントラル・リーグ 個人打撃成績（規定打席以上）
Reference: Central League individual batting result in fiscal year 2007(more than regulated at bat)

batting2007.csv
順位,打率,安打
Order, batting average, and safe hit
===
order,batting_avg,safe_hit
1,0.346,193
2,0.343,204
3,0.318,172
4,0.313,177
5,0.31,175
6,0.308,155
7,0.302,122
8,0.302,118
9,0.3,120
10,0.3,139
===

> data <- read.csv("batting2007.csv");
> data
order batting_avg safe_hit
1 1 0.346 193
2 2 0.343 204
3 3 0.318 172
4 4 0.313 177
5 5 0.310 175
6 6 0.308 155
7 7 0.302 122
8 8 0.302 118
9 9 0.300 120
10 10 0.300 139
>

ノーマル出力,Normal output

>plot(data$order, data$batting_avg)


両対数出力,Both logarithm output

>plot(data$order, data$batting_avg, log="xy")


y軸がlogになっていないような？
Isn't y axis log?
(2008/10/30)
データの幅が狭いと、対数にならない。
When the width of data is narrow, it doesn't become a logarithm.

~~~
[2]はじめから、LN計算してから、プロットする。
After LN is calculated from the start, it plots it.

常用対数,Common logarithm
>plot(log10(data$order), log10(data$batting_avg))


自然対数,Napierian logarithm
>plot(log(data$order), log(data$batting_avg))


これらもべき乗則になっています。
These are Power Laws.
~~~
end

Power Law:(11)Graph structure in the web

2008/11/01）
(google:power law)でヒットしたものでグラフありをチェック。第一弾。
(google:power law)It is checked that it is the one that became a hit and there is a graph. The first.

http://www9.org/w9cdrom/160/160.html
Graph structure in the web
Andrei Broder(1), Ravi Kumar(2), Farzin Maghoul(1),
Prabhakar Raghavan(2), Sridhar Rajagopalan(2), Raymie Stata(3),
Andrew Tomkins(2), Janet Wiener(3)

1: AltaVista Company, San Mateo, CA.
2: IBM Almaden Research Center, San Jose, CA.
3: Compaq Systems Research Center, Palo Alto, CA.
~~~


Fig.1のみをチェック。その他：Fig.2,3,4は未！TODO）
Only Fig.1 is checked. Additionally: Fig.2, 3, and 4 are unchecked. TODO)

~~~
直線部分のみの相対値を得る。
A relative value only of a straight line part is obtained.

A=-2.1

y=B*x^(A)
B=y/x^(A)
=1e6/10^(-2.1)
=1e6/7.943e-3
=0.126e9
=1.26e8

***
1=B*x^A
log1= logB + Alogx
-logB = Alogx

logx = (-logB)/A
x=10^((-logB)/A)
=7199.78

~~~
(x, y)=(10, 1e6),(7199.78, 1)
Relative value)
=(1, 1e6),(7199.78/10, 1)
=(1, 1e6),(719.98, 1)
A=-2.1
B=1e6

~~~
今回までのデータを示す。
Data until this time is shown.

"A","B","memo","Category"
-3.21,104660,"Power Law:(5),p.182,Fig.5-39(a)",Industry?
-2.457,4102.56,"Power Law:(5),p.182,Fig.5-39(b)",Industry?
-2.416,5.95e3,"Power Law:(5),p.182,Fig.5-39(c)",Industry?
-1.246,74,"Power Law:(5),p.128,Fig.4-14",Nature
-1.1818,5.337e4,"Power Law:(5),p.111,Fig.4-3",Electric
-1.092,24.926,"Power Law:(5),p.61,Fig.2-16(2)",Nature
-1.035,63.065,"Power Law:(5),p.123,Fig.4-10",Electric
-1.013,17.635,"Power Law:(5),p.63,Fig.2-18",Economy...human activity
-1.0123,20.75,"Power Law:(5),p.60,Fig.2-15",Economy...human activity
-1,1e4,"Power Law:(5),p.62,Fig.2-17",Culture?...human activity
-1.0,5.62e3,"Power Law:(5),p.175,Fig.5-33",Bio
-1,100,"Power Law:(5),p.125,Fig.4-12",Nature
-0.991,18.52,"Power Law:(5),p.61,Fig.2-16(1)",Nature
-0.767,200,"Power Law:(5),p.108,Fig.4-1",Electric
-0.353,58.214,"Power Law:(4),table.1",Bio
-0.29758,15.5,"Power Law:(3),p.242,Fig.44",Bio
-0.249,31.174,"Power Law:(7),p.27,Fig.3-1",Bio
-0.249,159.9,"Power Law:(7),p.36,Fig.3-2",Bio
-0.249,212.878,"Power Law:(7),p.36,Fig.3-2",Bio
-0.74,23.2,"Power Law:(8),p.22,Fig.2",Bio
-0.518,390,"Power Law:(8),p.24,Fig.3",Bio
-0.692,6.971e3,"Power Law:(8),p.26,Fig.4",Bio
-2.154,3162,"Power Law:(9),p.129,Fig.9",web...human activity
-6.179,1.234e5,"Power Law:(10),p.37,table",Nature...human
-2.1,1e6,"Power Law:(11),Fig.1",web...human activity
~~~
end

Power Law:(10)Chemical Element of Human

(2008/10/27)
KI図書館)
元素がわかる (ファーストブック) 小野 昌弘 (単行本（ソフトカバー） - 2008/8/23)
p.37,table,人間を作る元素の割合(体重70Kgの男性),Ratio of element that makes human(man of 70Kg in weight)





Excelで、LN-LNグラフを出力。いろいろやった近似式は以下。
：対象は、No.3からNo.20まで。
The LN-LN graph is output by Excel. The approximation type variously done is
the following.
The object : from No.3 to No.20.

LN(y)=-6.1803(LN(x))+17.03

LN
(x, y)=(3, 28008),(20, 0.227)
Relative value)
=(1, 28008/0.227),(20/3, 1)
=(1, 1.234e5),(6.667, 1)
A=-6.179
B=1.234e5

~~~
今回までのデータを示す。
Data until this time is shown.

"A","B","memo","Category"
-3.21,104660,"Power Law:(5),p.182,Fig.5-39(a)",Industry?
-2.457,4102.56,"Power Law:(5),p.182,Fig.5-39(b)",Industry?
-2.416,5.95e3,"Power Law:(5),p.182,Fig.5-39(c)",Industry?
-1.246,74,"Power Law:(5),p.128,Fig.4-14",Nature
-1.1818,5.337e4,"Power Law:(5),p.111,Fig.4-3",Electric
-1.092,24.926,"Power Law:(5),p.61,Fig.2-16(2)",Nature
-1.035,63.065,"Power Law:(5),p.123,Fig.4-10",Electric
-1.013,17.635,"Power Law:(5),p.63,Fig.2-18",Economy...human activity
-1.0123,20.75,"Power Law:(5),p.60,Fig.2-15",Economy...human activity
-1,1e4,"Power Law:(5),p.62,Fig.2-17",Culture?...human activity
-1.0,5.62e3,"Power Law:(5),p.175,Fig.5-33",Bio
-1,100,"Power Law:(5),p.125,Fig.4-12",Nature
-0.991,18.52,"Power Law:(5),p.61,Fig.2-16(1)",Nature
-0.767,200,"Power Law:(5),p.108,Fig.4-1",Electric
-0.353,58.214,"Power Law:(4),table.1",Bio
-0.29758,15.5,"Power Law:(3),p.242,Fig.44",Bio
-0.249,31.174,"Power Law:(7),p.27,Fig.3-1",Bio
-0.249,159.9,"Power Law:(7),p.36,Fig.3-2",Bio
-0.249,212.878,"Power Law:(7),p.36,Fig.3-2",Bio
-0.74,23.2,"Power Law:(8),p.22,Fig.2",Bio
-0.518,390,"Power Law:(8),p.24,Fig.3",Bio
-0.692,6.971e3,"Power Law:(8),p.26,Fig.4",Bio
-2.154,3162,"Power Law:(9),p.129,Fig.9",web...human activity
-6.179,1.234e5,"Power Law:(10),p.37,table",Nature...human
~~~
end

Power Law:(9)Nexus,Small Worlds ...

(2008/10/30)

KI図書館）
複雑な世界、単純な法則 ネットワーク科学の最前線 マーク・ブキャナン 阪本 芳久 (単行本 - 2005/2/25)
Nexus: Small Worlds and the Groundbreaking Science of Networks by Mark Buchanan

p.129,Fig.9,インターネットのノード分布,Node distribution of the Internet



~~~
reading point in figure) as memo.
y:6/12->10^(6/12)->3.162*1e3
x:15/24->10^(15/24)->4.217*1e1
~~~
log
(x, y)=(1, 3.162e3),(4.217e1, 1)
A=-2.154
B=3162

~~~
今回までのデータを示す。
Data until this time is shown.

"A","B","memo","Category"
-3.21,104660,"Power Law:(5),p.182,Fig.5-39(a)",Industry?
-2.457,4102.56,"Power Law:(5),p.182,Fig.5-39(b)",Industry?
-2.416,5.95e3,"Power Law:(5),p.182,Fig.5-39(c)",Industry?
-1.246,74,"Power Law:(5),p.128,Fig.4-14",Nature
-1.1818,5.337e4,"Power Law:(5),p.111,Fig.4-3",Electric
-1.092,24.926,"Power Law:(5),p.61,Fig.2-16(2)",Nature
-1.035,63.065,"Power Law:(5),p.123,Fig.4-10",Electric
-1.013,17.635,"Power Law:(5),p.63,Fig.2-18",Economy...human activity
-1.0123,20.75,"Power Law:(5),p.60,Fig.2-15",Economy...human activity
-1,1e4,"Power Law:(5),p.62,Fig.2-17",Culture?...human activity
-1.0,5.62e3,"Power Law:(5),p.175,Fig.5-33",Bio
-1,100,"Power Law:(5),p.125,Fig.4-12",Nature
-0.991,18.52,"Power Law:(5),p.61,Fig.2-16(1)",Nature
-0.767,200,"Power Law:(5),p.108,Fig.4-1",Electric
-0.353,58.214,"Power Law:(4),table.1",Bio
-0.29758,15.5,"Power Law:(3),p.242,Fig.44",Bio
-0.249,31.174,"Power Law:(7),p.27,Fig.3-1",Bio
-0.249,159.9,"Power Law:(7),p.36,Fig.3-2",Bio
-0.249,212.878,"Power Law:(7),p.36,Fig.3-2",Bio
-0.74,23.2,"Power Law:(8),p.22,Fig.2",Bio
-0.518,390,"Power Law:(8),p.24,Fig.3",Bio
-0.692,6.971e3,"Power Law:(8),p.26,Fig.4",Bio
-2.154,3162,"Power Law:(9),p.129,Fig.9",web...human activity
~~~
end

Power Law:(8)Biological Diversity,生物多様性

(2008/10/27,10/28)
べき乗パターンを収集中。
The patterns of Power Law are being collected.

またまた、べき乗の別なパターンを発見！
アレニウスです。アレニウスの式が出てきました。
結局、いろいろな人が発見して、同じ現象？に異なる名前が付けられてしまった？
Another pattern of the Power Law is discovered again.
It is Arrhenius. Arrhenius equation has come out.
After all, various people discover, and a different name has been named to the same phenomenon?

KI図書館)
なぜたくさんの生物がいるのか? (地球を丸ごと考える) 橘川 次郎 (単行本 - 1995/9)
~~~
抜粋）：読み未完了！(p.46,exit)
(p.vi)
多様ということは、無秩序につながるものではない。生物の集団は無作為に集められた種類から
構成されているのではなく、そこには必ず何らかの秩序がある。今日見られる生物の集団は、
起源を異にする個々の種が、分散や自然淘汰の結果、ある地域に共存するようになったもので、
その進化の過程は今もなお進行中である。このような意味で、多様性とは長い生物進化の歴史に
よってつちかわれた産物であり、、、

(p.vii)
自然界が多様であることによって、生物界の秩序が保たれているとすれば、その破壊を招く
人間の行為は、地球上の生物種全体の存続にマイナスのはたらきをすることになる。そこから
自然保護の倫理が生まれてくる。今や生命の多様性を保つために、全人類が責任を果たさなければ
ならない時代になってきた。

(p.22)
面積と種数の関係は、多様性を調べる際の基礎として役立つだけではない。この関係は、
生物の生息地がだんだん小さくなるにつれてどのくらいの種が絶滅するかを推定する基準と
しても用いられている。

(p.45)
自然界では、個体数の多い種や少ない種が、それぞれ振幅の異なる変動をしながら共存している。

~~~
[1]p.22,Fig.2,アレニウス方程式で表される植物の種数(S)と面積(A)の関係,
Relation between number of species and area of plant shown by Arrhenius equation

実データかは不明？出典不明？
Is it uncertain whether it is real data? Is the source uncertain?




S=13*A^(0.26)

(x, y)=(1, 13),(70, 39.2)
converts it)
(x, y/x)=(1, 13),(70, 39.2/70)
=(1, 13),(70, 0.56)
Relative value)
=(1, 13),(70, 0.56)
=(1, 13/0.56),(70, 1)
=(1, 23.2),(70, 1)
A=-0.74
B=23.2
~~~
[2]p.24,Fig.3,鳥の種数と面積との関係(対数表示)。
直線は、福島県以上の値をアレニウス方程式にあてはめたもの,
Relation between number of species and area of bird (logarithm display).
The straight line is an application of the value more than Fukushima Prefecture
to the Arrhenius equation.

~~~
reading point in figure) as memo.
y:10mm/13.5mm->10^(10/13.5)->5.5*1e3
y:4.5/13.5->10^(4.5/13.5)->2.15*1e1
~~~
log
(x, y)=(1e3, 2.15e1),(1e8, 5.5e3)
converts it)
(x, y/x)=(1e3, 2.15e1/1e3),(1e8, 5.5e3/1e8)
=(1e3, 2.15e-2),(1e8, 5.5e-5)
Relative value)
=(1, 2.15e-2/5.5e-5),(1e8/1e3, 1)
=(1, 0.39e3),(1e5, 1)
A=-0.518
B=0.39e3=390
~~~
[3]p.26,Fig.4,日本の3県とコスタリカを出発点とした場合の、鳥の種数と面積との関係(対数表示),
Relation between number of species and area of bird when three prefectures in Japan and CostaRica are made starting point(logarithm display)

~~~
reading point in figure) as memo.
y:12.5/14->10^(12.5/14)->7.814*1e3
y:2.5/14->10^(2.5/14)->1.509*1e2
x:4.3/7->10^(4.3/7)->4.11*1e2
x:1.2/7->10^(1.2/7)->1.484*1e8
~~~
log
(x, y)=(4.11e2, 1.509e2),(1.484e8, 7.814e3)
converts it)
(x, y/x)=(4.11e2, 1.509e2/4.11e2),(1.484e8, 7.814e3/1.484e8)
=(4.11e2, 0.367),(1.484e8, 5.265e-5)
Relative value)
=(1, 0.367/5.265e-5),(1.484e8/4.11e2, 1)
=(1, 6.971e3),(0.361e6, 1)
A=-0.692
B=6.971e3
~~~
今回までのデータを示す。
Data until this time is shown.

"A","B","memo","Category"
-3.21,104660,"Power Law:(5),p.182,Fig.5-39(a)",Industry?
-2.457,4102.56,"Power Law:(5),p.182,Fig.5-39(b)",Industry?
-2.416,5.95e3,"Power Law:(5),p.182,Fig.5-39(c)",Industry?
-1.246,74,"Power Law:(5),p.128,Fig.4-14",Nature
-1.1818,5.337e4,"Power Law:(5),p.111,Fig.4-3",Electric
-1.092,24.926,"Power Law:(5),p.61,Fig.2-16(2)",Nature
-1.035,63.065,"Power Law:(5),p.123,Fig.4-10",Electric
-1.013,17.635,"Power Law:(5),p.63,Fig.2-18",Economy...human activity
-1.0123,20.75,"Power Law:(5),p.60,Fig.2-15",Economy...human activity
-1,1e4,"Power Law:(5),p.62,Fig.2-17",Culture?...human activity
-1.0,5.62e3,"Power Law:(5),p.175,Fig.5-33",Bio
-1,100,"Power Law:(5),p.125,Fig.4-12",Nature
-0.991,18.52,"Power Law:(5),p.61,Fig.2-16(1)",Nature
-0.767,200,"Power Law:(5),p.108,Fig.4-1",Electric
-0.353,58.214,"Power Law:(4),table.1",Bio
-0.29758,15.5,"Power Law:(3),p.242,Fig.44",Bio
-0.249,31.174,"Power Law:(7),p.27,Fig.3-1",Bio
-0.249,159.9,"Power Law:(7),p.36,Fig.3-2",Bio
-0.249,212.878,"Power Law:(7),p.36,Fig.3-2",Bio
-0.74,23.2,"Power Law:(8),p.22,Fig.2",Bio
-0.518,390,"Power Law:(8),p.24,Fig.3",Bio
-0.692,6.971e3,"Power Law:(8),p.26,Fig.4",Bio
~~~
end

Fibonacci Again...

(2008/10/19)
子供と近くの「さとらんど」にいく。
http://www.satoland.com/

朝一番から、昼間まで数時間。ゼロ円で遊ぶ。ガソリン代は除く。
：さすがに、ゼロ円では厳しいか？子供のみ「引き馬」で、200円。

駐車料が無料なのがうれしい。
：だいぶ前は、500円/日だった。民間に委託されて無料になった。

草むしり、やぎや羊、馬？にえさやり。
私はむしり役。
さすがにこの時期は、広葉樹のはっぱも落ち始めている、、、
えんえんと草むしりをやっているうちに、ふと、たんぽぽが目につく。




たんぽぽの綿毛をとると、でました。



フィボナッチ数(Fibonacci number)。
渦が見えますか？自然はすばらしい。
~~~
end