〜スーパーバラ曲線を作ろう〜

※図でcanvasを使っています。IE9以上が必要です。無い人はchromeかfirefoxをダウンロードすれば見れます（無料）



〜円〜

バラ曲線の前に円を描いてみます

x=sin(r1)
y=cos(r1)

この式でr1に一定の値を足していきながらx,yに点を打っていくと円になります



x,yが-1〜1の間で変化するのでそれを座標に直します





〜基本的なバラ曲線〜

円に波形をかけるとバラ曲線になります　式は

x=sin(r2)*sin(r1)
y=sin(r2)*cos(r1)

です

sin(r2)を二回計算しないように直すと

a=sin(r2)
x=a*sin(r1)
y=a*cos(r1)

となります

r1に足してく値をt1、r2に足してく値をt2として

t1=1、t2=4でこうなります







〜中心から浮かせる〜

基本的なバラ曲線は中心が濃くなってしまうので波を浮かせてみます

波形は-1〜1で変化しているので1以下をかけて+1することで浮きます

a=sin(r2)*h2+1
x=a*sin(r1)
y=a*cos(r1)

h2は1以下の適当な数を入れます

t1=0.1　t2=1　h2=0.5でこうなります







t1とt2の比率を変えてみます



t1=0.4;　t2=1;


t1=0.7;　t2=1;







〜ぶっとくする〜

ここまでは

円×波形

でしたがこれを

円×波形＋小さい円

にするとぶっとくなります　式にすると

a=sin(r2)*h2+1
x=a*sin(r1)+sin(r3)*h3
y=a*cos(r1)+cos(r3)*h3

になります

r3に追加していく値t3はt1、t2とはなるべく無関係な数字にします

小円の半径h3はh2より小さい値が望ましいです


t1=0.2;　t2=1;　t3=2.1111;　h2=0.5;　h3=0.2;

〜太さを周期的に変える〜

小円の半径にも波をかけると太さが周期的に変わります

式にすると

a=sin(r2)*h2+1
x=a*sin(r1)+sin(r3)*h3*sin(r2)
y=a*cos(r1)+cos(r3)*h3*sin(r2)

です

sin(r2)を何度も計算しないように直すと

b=sin(r2)
a=b*h2+1
x=a*sin(r1)+sin(r3)*h3*b
y=a*cos(r1)+cos(r3)*h3*b

となります


t1=0.2;　t2=1;　t3=2.1111;　h2=0.5;　h3=0.2;






小円を収縮させるところを逆にしてみます

前の式でbは-1〜1で変化しているので1-abs(b)で小円が小さくなるところが逆になります つまり

b=sin(r2)
a=b*h2+1
c=1-abs(b)
x=a*sin(r1)+sin(r3)*h3*c
y=a*cos(r1)+cos(r3)*h3*c

でやるとこうなります


t1=0.2;　t2=1;　t3=2.1111;　h2=0.5;　h3=0.2;

値によって中にn芒星が出ます



〜花びら〜

波形をabs(sin(r2))にすると花びらっぽくなります

b=abs(sin(r2))
a=b*h2+1
x=a*sin(r1)
y=a*cos(r1)

t1=0.2;　t2=1;　h2=0.5;




波形を1-abs(b)にするとギザギザします

b=1-abs(sin(r2))
a=b*h2+1
x=a*sin(r1)
y=a*cos(r1)

t1=0.2;　t2=1;　h2=0.5;


太さをつけて1-bを小円にかけてみます

b=1-abs(sin(r2))
a=b*h2+1
c=1-b x=a*sin(r1)+sin(r3)*h3*c
y=a*cos(r1)+sin(r3)*h3*c

t1=0.25;　t2=1;　t3=2.1111;　h2=0.5;　h3=0.2;

値によって外側にn芒星が出ます



〜波を足す〜

別の周期の波を足してみます

足す波のラジアンはr2の奇数倍にします

b=(sin(r2)+sin(r2*3))/2　でかくなるので足した分だけ割る
a=b*h2+1
x=a*sin(r1)
y=a*cos(r1)

t1=0.2;　t2=1;　h2=0.5;


偶数倍だとこうなります

b=(sin(r2)+sin(r2*2))/2
a=b*h2+1
x=a*sin(r1)
y=a*cos(r1)

t1=0.2;　t2=1;　h2=0.5;

波の左右対称性が崩れてしまいますね


cosを足す場合は逆に偶数倍のほうがいいです

b=(sin(r2)+cos(r2*2))/2
a=b*h2+1
x=a*sin(r1)
y=a*cos(r1)

t1=0.2;　t2=1;　h2=0.5;





〜波を広げる〜

大きい円のラジアンにcos(r2*奇数)を足すと波が広がります

偶数倍だと崩れます

b=sin(r2)
a=b*h2+1
c=cos(r2)
x=a*sin(r1+c)
y=a*cos(r1+c)

t1=0.2;　t2=1;　h2=0.5;


変化が大きいので適当な数で割ったほうがいいです

b=sin(r2)
a=b*h2+1
c=cos(r2*3)/3
x=a*sin(r1+c)
y=a*cos(r1+c)

t1=0.2;　t2=1;　h2=0.5;


下のように足したり引いたりしてもよいです

b=sin(r2)
a=b*h2+1
c=(cos(r2*3)-cos(r2*5))/5
x=a*sin(r1+c)
y=a*cos(r1+c)

t1=0.2;　t2=1;　h2=0.5;






〜中ぐらいの円をつける〜

太くする小円とは別に中円をつけてみます

（大円＋中円）×波＋小円

って感じでつけます

中円のラジアンr4に追加する値t4はt1とt2から特定の値を出します　それは

t4=？*t2+t1

です

？は偶数ならなんでもよいです

中円の半径h4はh2とh3の間がよいです

b=sin(r2)
a=b*h2+1
x=a*(sin(r1)+sin(r4)*h4)
y=a*(cos(r1)+cos(r4)*h4)

t1=0.2;　t2=1;　t4=2*t2+t1;　h2=0.5;　h4=0.3;


複数つけてみます

b=sin(r2)
a=b*h2+1
x=a*(sin(r1)+sin(r4)*h4+sin(r5)*h5)
y=a*(cos(r1)+cos(r4)*h4+cos(r5)*h5)

t1=0.2;　t2=1;　t4=2*t2+t1;　t5=4*t2+t1;　h2=0.5;　h4=0.4;　h5=0.3;


〜激しく収縮させる〜

まずここまでのテクを複合してみます

b=(sin(r2*3)-sin(r2*5))/2
a=b*h2+1
c=cos(r2)/3
x=a*(sin(r1-c)+sin(r4)*h4)+sin(r3)*h3*b
y=a*(cos(r1-c)+cos(r4)*h4)+cos(r3)*h3*b

t1=0.2;　t2=1;　t3=2.1111;　t4=2*t2+t1;　h2=0.5;　h3=0.2;　h4=0.4;


小円の大きさが0になる所が数箇所ですがこれを8倍にしてみます

bが-1〜1の範囲で変化していますがこれを

b=abs(b)*8

これで0〜8になり

b=b%2

これで0〜2になり（ただし2から0への変化は値が跳躍）

if(b>1)b=2-b

これで0〜1間を折り返します


b=(sin(r2*3)-sin(r2*5))/2
a=b*h2+1
b=(abs(b)*8)%2
if(b>1)b=2-b
c=cos(r2)/3
x=a*(sin(r1-c)+sin(r4)*h4)+sin(r3)*h3*b
y=a*(cos(r1-c)+cos(r4)*h4)+cos(r3)*h3*b

t1=0.2;　t2=1;　t3=2.1111;　t4=2*t2+t1;　h2=0.5;　h3=0.2;　h4=0.4;


さらに(1-小円の収縮率)を波の広がりと中円の大きさにかけてみます

b=(sin(r2*3)-sin(r2*5))/2
a=b*h2+1
b=(abs(b)*8)%2
if(b>1)b=2-b
d=1-b
c=cos(r2)/3*d
x=a*(sin(r1-c)+sin(r4)*h4*d)+sin(r3)*h3*b
y=a*(cos(r1-c)+cos(r4)*h4*d)+cos(r3)*h3*b

t1=0.2;　t2=1;　t3=2.1111;　t4=2*t2+t1;　h2=0.5;　h3=0.2;　h4=0.4;


かなり密な図形になりましたね

小円の収縮に合わせて中円が動くのでいい感じの模様になります

これでテクは全部です

あとは適当にpowしたりsinの中でcosしたりいろいろ試してみてください



〜魔神タイプ〜

円をベースにしてきましたが

x=sin(r1*?)
y=cos(r1*?)

をベースにすると人っぽい形ができます

（ただしこれはバラ曲線とは呼べません 波の左右対称性ではなく全体の左右対称性を考えるため法則も変わってきます）

b=-sin(r2*3);
a=b*h2+1;
d=(abs(b)*5)%2;
if(d>1)d=2-d;
e=1-d;
c=cos(r2*3)/3;
x=a*(sin(r1*2-c)+sin(r4)/4*e)+sin(r3)*h3*d;
y=a*(cos(r1*3-c)+cos(r4)/4*e)+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.4; h3=0.1;
t4=4*t2+t1;

このタイプはまだ研究中です

t2/t1が非整数、2*t2/t1が整数になるようにすると左右対称になりやすいようです

中円の法則はまだよく分かりません



〜エディター〜

ここで直接式と値を打ち込んで描画できます

〜設定できる値〜

max・・・点の個数
ki・・・点の明るさ
tate,yoko・・・画面サイズ
han・・・全体の大きさ
tx,ty・・・中心座標　省略で真ん中
t1〜t6・・・r1〜r6に加算してく値
h2〜h6・・・式内で好きに使う用
col・・・色の配列　col=new Array(赤1,緑1,青1, 赤2,緑2,青2,・・)と指定する
　省略で(255,105,15,　255,105,15,　255,225,113)が入る

↓ここでパラメーターを設定してね
　











式をランダムに決めてスタート

タイプ１・・花弁が左右対称　　非常に形が整いやすいです
タイプ２・・全体が左右対称　　10回に一回ぐらいでいいのが出ます
タイプ３・・フリーダム　　　　100回に一回ぐらいでいいのが出ます


こいつで一度に大量のスーパーバラ曲線をランダムに作れます
↓ 〜スーパーバラ曲線量産機〜
http://www42.atwiki.jp/syugyou?cmd=upload&act=open&pageid=250&file=bar2.html

↓ここで式を設定してね





式で使える関数・・・javascriptで使えるもの全部
sin,cos,abs,powはMath.を省略可
変数はa〜wまで




〜遊び方〜

適当に式をいじって偶然からいい形のスーパーバラ曲線を発見します

いい形ができたら画面サイズと全体のおおきさとmaxを増やしてkiで色の濃さを調整

色の濃さが合ったら一気にmaxの桁を増やしその分kiの桁を減らします

maxがでかいほど綺麗になりますが1000万を超えたあたりから誤差による回転ブレが見えてしまいます

canvasを右クリック、もしくは小窓で表示させてから右クリックで保存できます



〜用語集〜

俺の脳内で勝手に使ってる用語です

山　・・・　円周上でぴったり一周するまでの波形の周期の数　t1=0.2 t2=1 → 5山　t1=0.7 t2=1 → 10山

星　・・・　太さが0になる個所

骨　・・・　太さを考慮しないときの軌道

浮かす　・・・　骨が中心を通らないようにさせること　基本

回す　・・・　t2/t1を非整数にすること

幼形　・・・　maxが低い時にのみいい感じの模様が出てること

バケ　・・・　波が左右対称でない図形

バミる　・・・　星周辺でアンチエイリアスがうまくいってないこと

チート　・・・　骨が連続してないこと

魔神タイプ　・・・　ベースが円形じゃないやつで人型っぽい図形

走る　・・・　maxをあげすぎてブレること





〜カオスも作れます〜

エディターでは前の座標が大文字のX,Yに格納されるのでこれを式内で使うと

カオスも作ることが可能です

パラメーターでX,Yの初期値も設定できます（省略で0）

※バラ曲線自体は確実にいつか元の位置に戻るのでカオスではありません

クリフォードアトラクタ
x=sin(t1*Y)+t3*cos(t1*X);
y=sin(t2*X)+t4*cos(t2*Y);

t1=-2; t2=2; t3=1; t4=1;



〜リンク〜

点を打つ処理はここを参照してください

〜canvasアナログ描画入門〜
http://www42.atwiki.jp/syugyou?cmd=upload&act=open&pageid=250&file=ana.html

座標の少数点位置によって周囲4ピクセルに光を振り分けます（バイリニア補間？）






カラパイアに載ったよ！

数学ってアート！方程式で描くゴージャスな「バラ曲線」で大魔神を描いてみた
http://karapaia.livedoor.biz/archives/52090692.html


youtube

〜スーパーバラ曲線を作ろう〜
http://www.youtube.com/watch?v=TAtMEz-gRi0

【魔神曲線】　〜計算から魔神を作ろう〜
http://www.youtube.com/watch?v=Y6US1bvnY8A

【魔神曲線】　〜計算から魔神を作ろう２〜
http://www.youtube.com/watch?v=JKwJiToVW04

【魔神曲線】　〜計算から魔神を作ろう３〜
http://www.youtube.com/watch?v=wcVe5J-e6UY



〜ギャラリー〜

スタートを押すと表示されます（すべて表示するまで時間がかかります）




b=sin(r2)+sin(r2)*3;
a=b*h2+1;
x=a*sin(r1)+sin(r3)*b;
y=a*cos(r1)+cos(r3)*b;

t1=0.3; t2=1; t3=2.11;
h2=0.6; h3=0.1;



b=(sin(r2*9)+sin(r2*7))/2;
d=(1-abs(b))*b;
a=b*h2+1;
c=cos(r2*3);
x=a*sin(r1+c)+sin(r3)*h3*d;
y=a*cos(r1+c)+cos(r3)*h3*d;

t1=0.1; t2=1; t3=2.1111;
h2=0.7; h3=0.1;





c=sin(r2)+sin(r2/2);
b=sin(r2+sin(c*2));
a=b*h2+1;
x=a*cos(r1)+cos(r3)*h3*c;
y=a*sin(r1)+sin(r3)*h3*c;

t1=0.2; t2=1; t3=3.1929229;
h2=0.7; h3=0.2;




b=(sin(r2*11)-sin(r2*7))/2;
d=(b*4)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=(cos(r2*5)+cos(r2*9))/2;
x=a*sin(r1+c)+sin(r3)*h3*d;
y=a*cos(r1+c)+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.7; h3=0.1;



b=(sin(r2*3)-sin(r2*5))/2;
d=(abs(b)*5)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=cos(r2);
e=1-d;
x=a*(sin(r1+c/3)+sin(r4)/3*d)
　+sin(r3)*h3*e;
y=a*(cos(r1+c/3)+cos(r4)/3*d)
　+cos(r3)*h3*e;

t1=0.1; t2=1; t3=2.1111;
h2=0.4; h3=0.1; t4=2*t2+t1;



b=(sin(r2*11)-sin(r2*9))/2;
d=(abs(b)*3)%2;
if(d>1)d=2-d;
a=b*h2+1;
e=1-d;
x=a*(sin(r1)+sin(r4)/2*d)
　+sin(r3)*h3*e;
y=a*(cos(r1)+cos(r4)/2*d)
　+cos(r3)*h3*e;

t1=0.25; t2=1; t3=2.1111;
h2=0.5; h3=0.1; t4=2*t2+t1;




b=sin(r2);
d=(abs(b)*6)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=r1-cos(r2)/4;
e=1-d;
x=a*(sin(c)+(sin(r4)/2)*d)
　+sin(r3)*h3*e;
y=a*(cos(c)+(cos(r4)/2)*d)
　+cos(r3)*h3*e;

t1=0.2; t2=1; t3=2.1111;
h2=0.4; h3=0.05; t4=4*t2+t1;




b=sin(r2);
d=(abs(b)*16)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=r1+cos(r2)/2;
e=1-d;
x=a*(sin(c)+(sin(r4)/4)*d
　+sin(r5)/12*e)+sin(r3)*h3*e;
y=a*(cos(c)+(cos(r4)/4)*d
　+cos(r5)/12*e)+cos(r3)*h3*e;

t1=0.7; t2=1; t3=2.1111;
h2=0.5; h3=0.04; t4=8*t2+t1;
t5=18*t2+t1;





b=(sin(r2)+cos(r2*2))/2;
d=(abs(b)*5)%2;
if(d>1)d=2-d;
a=b*h2+1;
e=1-d;
c=r1+cos(r2*5)/5*e;
x=a*(sin(c)+sin(r4)/4*e)
　+sin(r3)*h3*d;
y=a*(cos(c)+cos(r4)/4*e)
　+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.3; t4=2*t2+t1;



b=(sin(r2)-sin(r2*5)+sin(r2*7))/3;
a=b*h2+1;
d=((1-abs(b))*7)%2;
if(d>1)d=2-d;
e=1-d;
e*=e;
c=(cos(r2)+cos(r2*5)*e
　-cos(r2*7)*d)/3;
f=r1-c*e*d;
x=a*(sin(f)+sin(r4+c)/2*e)
　+sin(r3)*h3*d;
y=a*(cos(f)+cos(r4+c)/2*e)
　+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.7; h3=0.05; t4=2*t2+t1;



b=sin(r2);
d=(abs(b)*61)%2;
if(d>1)d=2-d;
a=b*h2+1;
e=d-0.5;
c=cos(r2*5)/2*e;
x=a*(sin(r1-c)+sin(r5)/2*e
　+sin(r4)/3*e)+sin(r3)*h3*d;
y=a*(cos(r1-c)+cos(r5)/2*e
　+cos(r4)/3*e)+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.1; t4=t2*2+t1;
t5=6*t2+t1;



b=sin(r2*3);
a=b*h2+1;
d=(pow(abs(b),5)*7)%2;
if(d>1)d=2-d;
e=1-d;
c=cos(r2*11)/4*e;
x=a*sin(r1*2+c)+sin(r4)/4*e
　+sin(r3)*h3*d;
y=a*cos(r1*3+c)+cos(r4)/4*e
　+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=6*t2+t1;



b=(sin(r2*3)+sin(r2*7))/2;
a=b*h2+1;
d=((1-b*b)*33)%2;
if(d>1)d=2-d;
e=1-d;
c=cos(r2*7)/2;
x=a*sin(r1*2+c)-sin(r4)/3*d
　+sin(r3)*h3*e;
y=a*cos(r1*3+c)-cos(r4)/3*d
　+cos(r3)*h3*e;

t1=0.2; t2=0.3; t3=2.1111;
h2=0.2; h3=0.1;
t4=4*t2+t1;



b=sin(r2*5)-sin(r2*7);
d=(abs(b)*3)%2;
if(d>1)d=2-d;
e=1-d;
c=sin(r2*7)/3*e;
x=sin(r1+c)-sin(r4)/3*d
+sin(r5)/10*d+sin(r3)*h3*e;
y=(cos(r1*4+c)*2-cos(r1*2+c))/3
-cos(r4)/3*d+cos(r5)/10*d
+cos(r3)*h3*e;

t1=0.1; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=2*t2+t1;
t5=-6*t2+t1;





b=sin(r2*9);
d=(abs(b)*8)%2;
if(d>1)d=2-d;
e=d-1;
x=-sin(r1*3)-sin(r4)/5*e
　-sin(r5)/5*e+sin(r3)*h3*d;
y=cos(r1*7)-cos(r4)/5
　-cos(r5)/5*e+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h3=0.1; t4=3.8; t5=8.2;




b=(sin(r2*11)*4-sin(r2*5))/5;
d=(abs(b)*11)%2;
if(d>1)d=2-d;
e=1-d;
e=pow(e,0.4);d=1-e;
c=(cos(r2*5)+cos(r2))/4;
a=b*h2-1;
x=a*sin(r1*3+c)+sin(r4)/4*e
　+sin(r6)/6*e+sin(r3)*h3*d;
y=a*cos(r1*4+c)+cos(r5)/4*e
　+cos(r6)/6*e+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.3; h3=0.15;
t4=8.4; t5=7.6; t6=6.4;



b=sin(r2*5+cos(r2*11));
d=(abs(b)*15)%2;
if(d>1)d=2-d;
e=1-d;
e=pow(e,0.4);
d=1-e;
c=(cos(r2*7)+cos(r2*3))/8;
a=b*h2+1;
x=a*sin(r1*3+c)+sin(r6)/5*e
　+sin(r5)/5*e+sin(r3)*h3*d;
y=a*cos(r1*5+c)+cos(r4)/5*e
　+cos(r6)/5*e+cos(r3)*h3*d;

t1=0.4; t2=0.5; t3=2.1111;
h2=0.2; h3=0.1;
t4=6.6; t5=4.4; t6=6.4;



b=sin(sin(r2*7-cos(r2*13)));
d=(abs(b)*20)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.3);d=1-e;
c=sin(cos(r2*5)-cos(r2*9))/8;
a=b*h2+1;
x=a*(sin(r1*4+c)-sin(r4)/6*e)
　-sin(r5)/6*e
　+sin(r6)/6*e+sin(r3)*h3*d;
y=a*(cos(r1*9+c)-cos(r4)/6*e)
　+cos(r5)/6*e
　+cos(r6)/6*e+cos(r3)*h3*d;

t1=0.2; t2=0.7; t3=2.1111;
h2=0.2; h3=0.1;
t4=4; t5=6.8; t6=4.4;









製作中

苦情は　じゃがりきん　まで

b=sin(r2)+sin(r2*19/3);
a=b*h2+1;
x=a*cos(r1)+sin(r3)*h3*b;
y=a*sin(r1)+cos(r3)*h3*b;

t1=0.1; t2=1; t3=2.1121;
h2=0.3; h3=0.1;



b=(sin(r2)+sin(r2*7))/2;
d=(1-abs(b))*b;
a=b*h2+1;
c=cos(r2*9);
x=a*sin(r1+c)+sin(r3)*h3*d;
y=a*cos(r1+c)+cos(r3)*h3*d;

t1=0.1; t2=1; t3=2.1111;
h2=0.7; h3=0.1;



b=(sin(r2*7)+sin(r2*17))/2;
d=((1-abs(b))*6)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=cos(r2*5);
x=a*sin(r1+c)+sin(r3)*h3*d;
y=a*cos(r1+c)+cos(r3)*h3*d;

t1=0.1; t2=1; t3=2.1111;
h2=0.7; h3=0.05;




b=(sin(r2*7)-sin(r2*13))/2;
d=(b*4)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=(cos(r2*9)+cos(r2*11))/2;
x=a*sin(r1+c)+sin(r3)*h3*d;
y=a*cos(r1+c)+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.7; h3=0.1;



b=(sin(r2*5)-sin(r2*3))/2;
d=(abs(b)*3)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=(cos(r2*11)+cos(r2*7))/2;
e=1-d;
x=a*(sin(r1+c/3)+sin(r4)/2*d)
　+sin(r3)*h3*e;
y=a*(cos(r1+c/3)+cos(r4)/2*d)
　+cos(r3)*h3*e;

t1=0.7; t2=1; t3=2.1111;
h2=0.5; h3=0.03; t4=2*t2+t1;



b=sin(r2-cos(r2*5)*3);
d=(abs(cos(b))*4)%2;
if(d>1)d=2-d;
a=b*h2+1;
e=1-d;
x=a*(sin(r1)+sin(r4)/2*d)
　+sin(r3)*h3*e;
y=a*(cos(r1)+cos(r4)/2*d)
　+cos(r3)*h3*e;

t1=0.25; t2=1; t3=2.1111;
h2=0.5; h3=0.05; t4=2*t2+t1;




b=sin(r2);
d=(abs(b)*5)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=r1+cos(r2)/2;
e=1-d;
x=a*(sin(c)+(sin(r4)/3)*d)
　+sin(r3)*h3*e;
y=a*(cos(c)+(cos(r4)/3)*d)
　+cos(r3)*h3*e;

t1=0.2; t2=1; t3=2.1111;
h2=0.4; h3=0.1; t4=10*t2+t1;




b=sin(r2);
d=(abs(b)*5)%2;
if(d>1)d=2-d; 　d=1-d;
a=b*h2+1;
c=cos(r2+cos(r2*3)-cos(r2*5));
f=1-d;
x=a*(sin(r1+c/5)+(sin(r4)/4)*d)
　+sin(r3)*h3*f;
y=a*(cos(r1+c/5)+(cos(r4)/4)*d)
　+cos(r3)*h3*f;

t1=0.9; t2=1; t3=2.1111;
h2=0.5; h3=0.04; t4=8*t2+t1;



b=sin(r2);
d=(abs(b)*5)%2;
if(d>1)d=2-d;
d*=d;
a=b*h2+1;
c=cos(r2*3);
e=1-d;
e*=e;
f=r4+c*e*3;
x=a*(sin(r1-c)+sin(f)/3*e)
　+sin(r3)*h3*d;
y=a*(cos(r1-c)+cos(f)/3*e)
　+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.6; h3=0.07; t4=2*t2+t1;






b=(sin(r2)-sin(r2*5))/2;
a=b*h2+1;
d=((1-abs(b))*3)%2;
if(d>1)d=2-d;
e=(d-0.5)*2;
e*=e;
c=r1-(cos(r2*5)*(1-e)
　-cos(r2*3)*e)/7;
x=a*sin(c)+sin(r3)*h3*d;
y=a*cos(c)+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.8; h3=0.1;



b=(sin(r2*3)-sin(r2))/2;
a=b*h2+1;
d=(b*b*5)%2;
if(d>1)d=2-d;
e=1-d;
c=-cos(r2*3)/3*e;
x=a*(sin(r1-c)+sin(r4+c)*e/2)
　+sin(r3)*h3*d;
y=a*(cos(r1-c)+cos(r4+c)*e/2)
　+cos(r3)*h3*d;

t1=0.7; t2=1; t3=2.1111;
h2=0.5; h3=0.1; t4=2*t2+t1;





b=sin(r2*3);
d=(abs(b)*11)%2;
if(d>1)d=2-d;
e=1-d;
c=cos(r2*3)*1.5;
x=sin(r1)+sin(r4+c)/4*e
　+sin(r3)*h3*d;
y=sin(r2)-cos(r4+c)/4*e
　+cos(r3)*h3*d;

t1=0.4; t2=0.7; t3=2.1111;
h2=0.5; h3=0.1;
t4=6*t2+t1;




b=(cos(r2*11)-cos(r2*7))/2;
d=(abs(b)*10)%2;
if(d>1)d=2-d;
e=1-d;
a=b*h2+1;
x=-a*sin(r1*4)
　+sin(r4)/6*e+sin(r3)*h3*d
y=a*cos(r1*5)
　+cos(r4)/6*e+cos(r3)*h3*d

t1=0.3; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=-t2*5+t1;



b=cos(r2*7);
d=(abs(b)*8)%2;
if(d>1)d=2-d;
e=d-1;
c=sin(r2*6)/3;
x=sin(r1-c)+sin(r4)/3*e
-sin(r5)/5*e+sin(r3)*h3*d;
y=(cos(r1*4-c)-cos(r1*6-c)*2)/2
+cos(r4)/3*e-cos(r5)/5*e
+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.1; h3=0.1; t4=-6*t2+t1;
t5=3*t2+t1;




b=sin(r2*3);
d=(abs(b)*10)%2;
if(d>1)d=2-d;
e=1-d;
a=b*h2-1;
c=cos(r2*417)/3;
x=a*sin(r1*2)+sin(r4+c)/6
　+sin(r5+c)/6*e+sin(r3)*h3*d;
y=a*cos(r1*5)+cos(r4+c)/6
　+cos(r5+c)/6*e+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.3; h3=0.1;
t4=-9.6; t5=10.4;



b=(sin(r2)-sin(r2*5))/2;
a=b*h2-1;
d=(abs(b)*9)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.5);d=1-e;
c=cos(r2*3-cos(r2*5
　-cos(r2*9)*2)*2)/4;
x=a*sin(r1*4-c)+sin(r4)*e/4
　+sin(r3)*h3*d;
y=a*cos(r1*9-c)+cos(r4)*e/4
　+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.2; h3=0.1;
t4=5.6;



b=sin(r2*9-cos(r2*7));
d=(abs(b)*13)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.4);d=1-e;
c=(cos(r2*9)-cos(r2*11))/9;
a=b*h2-1;
x=a*(sin(r1*2+c)-sin(r4)/6*e)
　+sin(r5)/6*e
　+sin(r6)/6*e+sin(r3)*h3*d;
y=a*(cos(r1*7+c)+cos(r4)/6*e)
　+cos(r5)/6*e
　+cos(r6)/6*e+cos(r3)*h3*d;

t1=0.4; t2=0.9; t3=2.1111;
h2=0.2; h3=0.1;
t4=7.6; t5=9.4; t6=4;



b=sin(sin(r2*9+cos(r2*5))*3);
d=(abs(b)*18)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.4);d=1-e;
c=sin(cos(r2*11)*3-cos(r2*7)*3)/5;
a=b*h2+1;
x=a*(sin(r1*2+c)+sin(r4)/6*e)
　-sin(r5)/6*e
　-sin(r6)/6*e+sin(r3)*h3*d;
y=a*(cos(-r1*5+c)+cos(r4)/6*e)
　+cos(r5)/6*e
　-cos(r6)/6*e+cos(r3)*h3*d;

t1=0.4; t2=0.7; t3=2.1111;
h2=0.3; h3=0.1;
t4=7.4; t5=1.8; t6=1;



c=sin(r2);
b=(c+cos(r2*2))/2;
a=b*h2+1;
d=h3*b*c;
x=a*cos(r1)+sin(r3)*d;
y=a*sin(r1)+cos(r3)*d;

t1=0.9; t2=1; t3=2.1111;
h2=0.6; h3=0.2;



c=cos(r2*6);
b=(sin(r2)+c)/2;
c=1-abs(c);
a=b*h2+1;
x=a*cos(r1)+sin(r3)*h3*c;
y=a*sin(r1)+cos(r3)*h3*c;

t1=0.1; t2=1; t3=2.1111;
h2=1; h3=0.15;



b=(sin(r2)+sin(r2*23))/2;
d=((1-abs(b))*8)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=cos(r2*21);
x=a*sin(r1+c)+sin(r3)*h3*d;
y=a*cos(r1+c)+cos(r3)*h3*d;

t1=0.1; t2=1; t3=2.1111;
h2=0.7; h3=0.05;



b=sin(r2*2);
b=sin(r2+sin(b+sin(b)*3));
d=(b*4)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=cos(r2*3);
x=a*sin(r1+c/5)+sin(r3)*h3*d;
y=a*cos(r1+c/5)+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.7; h3=0.1;



b=(sin(r2*7)-sin(r2*3))/2;
d=(abs(b)*4)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=(cos(r2*5)+cos(r2*9))/2;
e=1-d;
x=a*(sin(r1+c/3)+sin(r4)/3*e*d)
　+sin(r3)*h3*e;
y=a*(cos(r1+c/3)+cos(r4)/3*e*d)
　+cos(r3)*h3*e;

t1=0.3; t2=1; t3=2.1111;
h2=0.5; h3=0.03; t4=2*t2+t1;



b=sin(r2); d=(abs(b)*3)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=cos(r2)/3+r1;
f=1-d;
x=a*(sin(c)+(sin(r4)/2
+sin(r5)/5)*d)+sin(r3)*h3*f;
y=a*(cos(c)+(cos(r4)/2
+cos(r5)/5)*d)+cos(r3)*h3*f;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.1; t4=2*t2+t1;
t5=6*t2+t1;



b=sin(r2);
d=(abs(b)*4)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=r1+cos(r2)/2;
e=1-d;
x=a*(sin(c)+(sin(r4)/4)*d)
　+sin(r3)*h3*e;
y=a*(cos(c)+(cos(r4)/4)*d)
　+cos(r3)*h3*e;

t1=0.3; t2=1; t3=2.1111;
h2=0.5; h3=0.04; t4=4*t2+t1;




b=sin(r2);
d=(abs(b)*3)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=cos(r2);
e=1-d;
x=a*(sin(r1+c/2)+(sin(r4))*d*e)
　+sin(r3)*h3*e;
y=a*(cos(r1+c/2)+(cos(r4))*d*e)
　+cos(r3)*h3*e;

t1=0.7; t2=1; t3=2.1111;
h2=0.5; h3=0.04; t4=4*t2+t1;





b=(sin(r2)+cos(r2*2))/2;
d=(abs(b)*7)%2;
if(d>1)d=2-d;
a=b*h2+1;
e=1-d;
e*=e*e*e;
c=r1+cos(r2*3)/5*e;
x=a*(sin(c)-sin(r4)/3*e)
　+sin(r3)*h3*d;
y=a*(cos(c)-cos(r4)/3*e)
　+cos(r3)*h3*d;

t1=0.7; t2=1; t3=2.1111;
h2=0.5; h3=0.07; t4=4*t2+t1;






b=(sin(r2)-cos(r2*2))/2;
a=b*h2+1;
d=(abs(b)*5)%2;
if(d>1)d=2-d;
e=(d-0.5)*2;
e=1-e*e;
x=a*(sin(r1)+sin(r4)/2*e)
　+sin(r3)*h3*d;
y=a*(cos(r1)+cos(r4)/2*e)
　+cos(r3)*h3*d;

t1=0.6; t2=1; t3=2.1111;
h2=0.5; h3=0.1; t4=4*t2+t1;



b=(sin(r2)+sin(r2*3)/2)/1.5;
a=b*h2+1;
d=(pow(abs(b),0.5)*31)%2;
if(d>1)d=2-d;
e=d+0.5;
c=r1-cos(r2*13)/9*e;
x=a*(sin(c)+sin(r4)/4*e
　+sin(r5)/3*d)+sin(r3)*h3*d;
y=a*(cos(c)+cos(r4)/4*e
　+cos(r5)/3*d)+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.5; h3=0.1; t4=4*t2+t1;
t5=10*t2+t1;




b=sin(r2*7);
d=(abs(b)*7)%2;
if(d>1)d=2-d;
e=d-1;
c=cos(r2*3)/5*e;
x=sin(r1+c)+sin(r4)/3*d
　-sin(r5)/4*e+sin(r3)*h3*e;
y=cos(r1*5-c)+cos(r4)/2*d
　+cos(r5)/3*e+cos(r3)*h3*e;

t1=0.8; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=6*t2+t1; t5=2*t2+t1;





b=sin(r2*7);
d=(abs(b)*17)%2;
if(d>1)d=2-d;
e=1-d;
x=sin(r1)-sin(r4)/2*d
　+sin(r5)/7*d+sin(r3)*h3*e;
y=cos(r1*7)+cos(r4)/2*d
　+cos(r5)/3*d+cos(r3)*h3*e;

t1=0.4; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=t2*4+t1; t5=t2*6+t1



b=(sin(r2)-sin(r2*3))/2;
a=b*h2+1;
d=(abs(b)*61)%2;
if(d>1)d=2-d;
e=1-d;
c=cos(r2*71)/4;
x=a*sin(r1*3-c)-sin(r4)/4*e
　+sin(r3)*h3*d;
y=-a*cos(r1+c)-cos(r4)/3*e
　+cos(r3)*h3*d;

t1=0.2; t2=0.3; t3=2.1111;
h2=0.65; h3=0.1;
t4=t2*6+t1;



b=(sin(r2*5)-sin(r2*9))/2;
d=(abs(b)*12)%2;
if(d>1)d=2-d;
e=1-d;
e=pow(e,0.5);d=1-e;
c=(cos(r2*7)-cos(r2))/5;
a=b*h2+1;
x=a*sin(r1*2+c)-sin(r4)/3*e
　+sin(r3)*h3*d;
y=a*cos(r1*7+c)-cos(r4)/3*e
　+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=6.4;



b=(sin(r2*5+cos(r2*7)/4)
　-sin(r2*17+cos(r2*11)/4))/2;
a=b*h2-1;d=(abs(b)*7)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.5);d=1-e;
c=cos(r2*3-cos(r2*5
　-cos(r2*11)*3)/2)/5;
x=a*sin(r1*3-c)+sin(r4)/5
　+sin(r5)/5*e+sin(r3)*h3*d;
y=a*cos(r1*8-c)+cos(r4)/5
　+cos(r5)/5*e+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.3; h3=0.1;
t4=-6.4; t5=-8.4;



b=sin(r2*7+cos(r2*3)*1.5);
d=(abs(b)*11)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.5);d=1-e;
c=(cos(r2*11)-cos(r2*5)/2)/8;
a=b*h2+1;
x=a*(sin(r1*2+c)+sin(r4)/6*e
　+sin(r5)/6*e)
　+sin(r6)/5*e+sin(r3)*h3*d;
y=a*(cos(r1*7+c)-cos(r4)/6*e
　-cos(r5)/6*e)
　+cos(r6)/5*e+cos(r3)*h3*d;

t1=0.2; t2=1.1; t3=2.1111;
h2=0.2; h3=0.1;
t4=2.4; t5=2; t6=6.4;



b=sin(sin(r2*3-cos(r2*7))*3);
d=(abs(b)*15)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.5);d=1-e;
c=sin(cos(r2*5)-cos(r2*11))/7;
a=b*h2-1;
x=a*(sin(r1*3+c)+sin(r4)/6*e)
　-sin(r5)/6*e
　-sin(r6)/6*e+sin(r3)*h3*d;
y=a*(cos(r1*7+c)+cos(r4)/6*e)
　+cos(r5)/6*e
　-cos(r6)/6*e+cos(r3)*h3*d;

t1=-0.2; t2=0.7; t3=2.1111;
h2=0.3; h3=0.1;
t4=2.6; t5=4; t6=5.4;




b=(sin(r2)-sin(r2*3))/2;
c=(1-abs(b));
a=b*h2+1;
x=a*sin(r1)+sin(r3)*h3*c;
y=a*cos(r1)+cos(r3)*h3*c;

t1=0.15; t2=1; t3=2.1111;
h2=0.7; h3=0.15;




c=sin(r2);
b=sin(r2+c);
a=b*h2+1;
x=a*sin(r1)+sin(r3)*h3*c;
y=a*cos(r1)+cos(r3)*h3*c;

t1=0.1; t2=1; t3=2.1121;
h2=0.7; h3=0.2;



b=sin(r2);
c=abs(b)*2;
if(c>1)c=2-c;
c=pow(c,2.5);
a=b*h2+1;
x=a*cos(r1)+cos(r3)*h3*c;
y=a*sin(r1)+sin(r3)*h3*c;

t1=0.1; t2=1; t3=2.115;
h2=0.5; h3=0.5;



b=sin(r2);
d=(abs(b)*5)%2;
if(d>1)d=2-d;
a=b*h2+1; c=1-d;
x=a*(sin(r1)+sin(r4)/3*d)
　+sin(r3)*h3*c;
y=a*(cos(r1)+cos(r4)/3*d)
　+cos(r3)*h3*c;

t1=0.1; t2=1; t3=2.1111;
h2=0.4; h3=0.1; t4=2*t2+t1;




b=sin(r2-cos(r2)*2);
d=(abs(b)*6)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=1-d;
x=a*(sin(r1)+sin(r4)/2*d)
　+sin(r3)*h3*c;
y=a*(cos(r1)+cos(r4)/2*d)
　+cos(r3)*h3*c;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.05; t4=2*t2+t1;



b=(sin(r2)-sin(r2*3))/2;
d=(abs(b)*5)%2;
if(d>1)d=2-d;
a=b*h2+1;
f=1-d;
x=a*(sin(r1)+(sin(r4)/2
　+sin(r5)/5)*d)+sin(r3)*h3*f;
y=a*(cos(r1)+(cos(r4)/2
　+cos(r5)/5)*d)+cos(r3)*h3*f;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.5; t4=2*t2+t1;
t5=6*t2+t1;



b=sin(r2*3);
d=(abs(b)*20)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=r1-cos(r2)/4;
e=1-d;
x=a*(sin(c)+(sin(r4)/3)*d)
　+sin(r3)*h3*e;
y=a*(cos(c)+(cos(r4)/3)*d)
　+cos(r3)*h3*e;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.04; t4=4*t2+t1;




b=sin(r2);
d=(abs(b)*5)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=r1-cos(r2)/4;
e=(1-d)*d;
x=a*(sin(c)+sin(r4)*e)
　+sin(r3)*h3*d;
y=a*(cos(c)+cos(r4)*e)
　+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.6; h3=0.1; t4=4*t2+t1;



b=(sin(r2)+sin(r2*3)/2)/1.5;
a=b*h2+1;
d=(abs(b)*7)%2;
if(d>1)d=2-d;
e=1-d;
e*=e*e;
c=(cos(r2+cos(r2*5)/3*d));
f=r1-c/3*e;
g=r4-c/2;
x=a*(sin(f)+sin(g)/2*d)
　+sin(r3)*h3*d;
y=a*(cos(f)+cos(g)/2*d)
　+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.6; h3=0.1; t4=6*t2+t1;




b=sin(r2);
a=b*h2+1;
d=(abs(b)*3)%2;
if(d>1)d=2-d;
e=(d-0.5)*2;
e=e*e;
c=r1-cos(r2*3)*e/4;
f=1-e;
x=a*(sin(c)+sin(r4)/2*e)
　+sin(r3)*h3*f;
y=a*(cos(c)+cos(r4)/2*e)
　+cos(r3)*h3*f;

t1=0.8; t2=1; t3=2.1111;
h2=0.5; h3=0.1; t4=2*t2+t1;



b=(sin(r2)-sin(r2*7)/4)/1.25;
d=(pow(abs(b),0.4)*12)%2;
if(d>1)d=2-d;
d*=d;
e=1-d; e*=e;
c=cos(r2*17)*e;
x=sin(r1)+sin(r4-c)/4
　*e+sin(r3)*h3*d;
y=sin(r2)+cos(r4-c)/4
　*e+cos(r3)*h3*d;

t1=0.2; t2=0.3; t3=2.1111;
h2=0.5; h3=0.2;
t4=4*t2+t1;



b=(sin(r2*3)*4-sin(r2*5))/5;
d=(pow(abs(b),0.4)*6)%2;
if(d>1)d=2-d;
e=1-d;
a=abs(b)*h2+0.5;
c=cos(r2*9)*e;
x=a*sin(r1*2)-sin(r4+c)/4*e
　+sin(r3)*h3*d;
y=cos(r1*3)+cos(r4-c)/3*e
　+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=2*t2+t1;




b=sin(r2*3);
d=(abs(b)*5)%2;
if(d>1)d=2-d;
e=1-d;
c=sin(r2)/2;
x=sin(r1*3-c)+sin(r4)/3*e
　+sin(r5)/5*e+sin(r3)*h3*d;
y=cos(r1-c)+cos(r4)/3*e
　+cos(r5)/5*e+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=-4*t2+t1;
t5=2*t2+t1;



b=sin(r2);
d=(abs(b)*21)%2;
if(d>1)d=2-d;
e=1-d;
c=cos(r2)/3;
x=sin(r1*4-c)-sin(r4)/3*e
　+sin(r5)/3*e+sin(r3)*h3*d;
y=cos(r1-c)-cos(r4)/3*e
　+cos(r5)/3*e+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=4.8; t5=-7.2;



b=(sin(r2*7)-sin(r2))/2;
d=(abs(b)*15)%2;
if(d>1)d=2-d;
e=1-d;
e=pow(e,0.4);d=1-e;
c=(cos(r2*13)-cos(r2*3))/7;
a=b*h2+1;
x=a*sin(r1+c)-sin(r4)/4*e
　+sin(r5)/4*e+sin(r3)*h3*d;
y=a*cos(r1*4+c)+cos(r4)/4*e
　+cos(r5)/4*e+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.3; h3=0.2;
t4=8.4; t5=10.4;



b=(sin(r2*5+cos(r2*9)*2)
　+sin(r2*7))/2;
d=(abs(b)*14)%2;
if(d>1)d=2-d; e=1-d;
e=pow(e,0.5);d=1-e;
c=(cos(r2*5)+cos(r2*13)/2)/8;
a=b*h2+1;
x=a*sin(r1*2+c)-sin(r4)/5*e
　+sin(r5)/5*e+sin(r3)*h3*d;
y=a*cos(r1*5+c)+cos(r4)/5*e
　+cos(r5)/5*e+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.2; h3=0.1;
t4=-10.8; t5=-5.6;



b=sin(sin(r2*5)-sin(r2*3));
d=(abs(b)*15)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.4);d=1-e;
c=sin(cos(r2*11)-cos(r2*7))/8;
a=b*h2+1;
x=a*(sin(r1*2+c)-sin(r4)/6)
　-sin(r5)/6*e
　+sin(r6)/6*e+sin(r3)*h3*d;
y=a*(cos(r1*5+c)+cos(r4)/6)
　+cos(r5)/6*e
　+cos(r6)/6*e+cos(r3)*h3*d;

t1=0.2; t2=0.7; t3=2.1111;
h2=0.2; h3=0.1;
t4=4.4; t5=3; t6=5.4;



b=sin(sin(r2*11-cos(r2*9))*3);
d=(abs(b)*15)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.4);d=1-e;
c=sin(cos(r2*7+cos(r2*5)*2)*2)/7;
a=b*h2+1;
x=a*(sin(r1*2+c)-sin(r4)/6*e)
　-sin(r5)/6*e
　+sin(r6)/6*e+sin(r3)*h3*d;
y=a*(cos(r1*9+c)-cos(r4)/6*e)
　+cos(r5)/6*e
　+cos(r6)/6*e+cos(r3)*h3*d;

t1=-0.2; t2=0.5; t3=2.1111;
h2=0.2; h3=0.1;
t4=3.2; t5=4.2; t6=1.2;



b=sin(r2);
c=1-abs(b);
a=b*h2+1;
d=cos(b);
x=a*sin(r1+d)+sin(r3)*h3*c;
y=a*cos(r1+d)+cos(r3)*h3*c;

t1=0.1; t2=1; t3=2.1111;
h2=0.5; h3=0.2;




c=sin(r2)+sin(r2*2);
b=sin(r2+c*2);
a=b*h2+1;
x=a*cos(r1)+cos(r3)*h3*c;
y=a*sin(r1)+sin(r3)*h3*c;

t1=0.1; t2=1; t3=2.1121;
h2=0.7; h3=0.2;



b=(sin(r2*3)-sin(r2*9))/2;
d=(b*4)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=(cos(r2*5)+cos(r2*7))/2;
x=a*sin(r1+c)+sin(r3)*h3*d;
y=a*cos(r1+c)+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.7; h3=0.1;



b=sin(r2);
d=(abs(b)*5)%2;
if(d>1)d=2-d; a=b*h2+1;
c=cos(r2); f=1-d;
x=a*(sin(r1+c/3)+sin(r4)/3*d)
　+sin(r3)*h3*f;
y=a*(cos(r1+c/3)+cos(r4)/3*d)
　+cos(r3)*h3*f;

t1=0.1; t2=1; t3=2.1111;
h2=0.4; h3=0.1; t4=2*t2+t1;



b=(sin(r2)-sin(r2*5))/2;
d=(abs(b)*5)%2;
if(d>1)d=2-d;
a=b*h2+1;
e=cos(r2);
e=1-d;
x=a*(sin(r1)+sin(r4)/2*d)
　+sin(r3)*h3*e;
y=a*(cos(r1)+cos(r4)/2*d)
　+cos(r3)*h3*e;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.1; t4=2*t2+t1;



b=(sin(r2*5)-sin(r2*3))/2;
d=(abs(b)*8)%2;
if(d>1)d=2-d;
a=b*h2+1;
e=1-d;
x=a*(sin(r1)+(sin(r4)/3)*d)
　+sin(r3)*h3*e;
y=a*(cos(r1)+(cos(r4)/3)*d)
　+cos(r3)*h3*e;

t1=0.2; t2=1; t3=2.1111;
h2=0.4; h3=0.1; t4=4*t2+t1;




b=sin(r2);
d=(abs(b)*7)%2;
if(d>1)d=2-d;
a=b*h2+1;
c=r1+cos(r2+cos(r2*7)/2)/2;
e=1-d;
x=a*(sin(c)+(sin(r4))*d*e)
+sin(r3)*h3*e;
y=a*(cos(c)+(cos(r4))*d*e)
+cos(r3)*h3*e;

t1=0.2; t2=1; t3=2.1111;
h2=0.7; h3=0.05; t4=4*t2+t1;



b=sin(r2);
d=(abs(b)*5)%2;
if(d>1)d=2-d;
a=b*h2+1;
e=1-d;
e=d*e*e*4; f=1-e;
c=r1-cos(r2*3)*f*f/2;
x=a*(sin(c)-sin(r4)/2*e)
　+sin(r3)*h3*d;
y=a*(cos(c)-cos(r4)/2*e)
　+cos(r3)*h3*d;

t1=0.2; t2=1; t3=2.1111;
h2=0.6; h3=0.07; t4=4*t2+t1;





b=sin(r2);
a=b*h2+1;
d=(abs(b)*8)%2;
if(d>1)d=2-d;
e=1-d;
e*=e*e;
c=(cos(r2)-cos(r2*3)*e)/3;
x=a*(sin(r1+c)+sin(r4+c)/2)
　+sin(r3)*h3*d;
y=a*(cos(r1+c)+cos(r4+c)/2)
　+cos(r3)*h3*d;

t1=0.002; t2=0.01; t3=2.1111;
h2=0.5; h3=0.1; t4=2*t2+t1;






b=(sin(r2)-sin(r2*5))/2;
a=b*h2+1;
d=(abs(b)*8)%2;
if(d>1)d=2-d;
e=(d-0.5)*2;
c=cos(r2*3-cos(r2*5))*e;
x=a*(sin(r1-c/4)+sin(r4+c)/2*d)
　+sin(r3)*h3*e;
y=a*(cos(r1-c/4)+cos(r4+c)/2*d)
　+cos(r3)*h3*e;

t1=0.2; t2=1; t3=2.1111;
h2=0.5; h3=0.05; t4=4*t2+t1;



b=(sin(r2*5)-sin(r2))/2;
d=(abs(b)*7)%2;
if(d>1)d=2-d;
d*=d;
e=1-d; e*=e;
c=cos(r2*7)*e;
x=sin(r1)+sin(r4+c)/3*e
　+sin(r3)*h3*d;
y=sin(r2)+cos(r4+c)/3*e
　+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.5; h3=0.2; t4=6*t2+t1;




b=(sin(r2*11)-sin(r2*9))/2;
a=b*h2+1;
d=(abs(b)*5)%2;
if(d>1)d=2-d;
e=1-d;
c=cos(r2*7)/2*d*e;
x=a*sin(r1*2-c)-sin(r4)/4*d
　+sin(r3)*h3*e;
y=a*cos(r1*3+c)+cos(r4)/4*d
　+cos(r3)*h3*e;

t1=0.4; t2=1; t3=2.1111;
h2=0.4; h3=0.1;
t4=2*t2+t1;



b=(sin(r2*3)-sin(r2*7));
d=(abs(b)*7)%2;
if(d>1)d=2-d;
e=d-1;
c=(sin(r2)-sin(r2*7))/2.5*d;
x=sin(r1+c)+sin(r4)/2*e
　+sin(r3)*h3*d;
y=cos(r1*6+c)+cos(r4)/2*e
　+cos(r3)*h3*d;
y=-y;

t1=0.6; t2=1; t3=2.1111;
h2=0.5; h3=0.1;
t4=t2*6+t1;



b=(sin(r2)+cos(r2*6))/2;
d=(abs(b)*16)%2;
if(d>1)d=2-d;
e=1-d;
e=pow(e,0.4);d=1-e;
a=b*h2+1;
x=a*sin(r1*2)-sin(r4)/4*e
　+sin(r3)*h3*d;
y=a*cos(r1*5)+cos(r4)/4*e
　+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.5; h3=0.15;
t4=-t2*10+t1;



b=(sin(r2*13)+sin(r2*7))/2;
d=(abs(b)*11)%2;
if(d>1)d=2-d;
e=1-d;
e=pow(e,0.5);d=1-e;
c=(cos(r2*9)-cos(r2))/10;
a=b*h2+1;
x=a*sin(r1-c)-sin(r4)/4*e
　+sin(r3)*h3*d;
y=a*cos(r1*5-c)-cos(r5)/3*e
　+cos(r3)*h3*d;

t1=0.4; t2=1; t3=2.1111;
h2=0.2; h3=0.1;
t4=6.4;t5=10.4;




b=sin(r2*5);
d=(b*b*11)%2;
if(d>1)d=2-d;
e=1-d;
x=sin(r1*3)+sin(r4)/5
　+sin(r5)/5*e
　+sin(r3)*h3*d;
y=cos(r1*5)-cos(r4)/5
　+cos(r5)/5*e
　+cos(r3)*h3*d;

t1=0.2; t2=0.7; t3=2.1111;
h3=0.1; t4=1.9; t5=5.8;




b=sin(sin(r2*11)-sin(r2*3));
d=(abs(b)*15)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.4);d=1-e;
c=sin(cos(r2*7-cos(r2*5)))/5;
a=b*h2+1;
x=a*(sin(r1*2+c)-sin(r4)/6)
　-sin(r5)/6*e
　+sin(r6)/6*e+sin(r3)*h3*d;
y=a*(cos(r1*9+c)+cos(r4)/6)
　-cos(r5)/6*e
　+cos(r6)/6*e+cos(r3)*h3*d;

t1=0.2; t2=0.5; t3=2.1111;
h2=0.1; h3=0.1;
t4=5.2; t5=4.8; t6=2.8;



b=sin(-(sin(r2*3)+sin(r2*9))*1.5);
d=(abs(b)*13)%2;
if(d>1)d=2-d;e=1-d;
e=pow(e,0.5);d=1-e;
c=sin((cos(r2*11)-cos(r2*7))*1.5)/7;
a=b*h2+1;
x=a*(sin(r1*2+c)-sin(r4)/6*e)
　-sin(r5)/6*e
　+sin(r6)/6*e+sin(r3)*h3*d;
y=a*(cos(r1*9+c)-cos(r4)/6*e)
　+cos(r5)/6*e
　+cos(r6)/6*e+cos(r3)*h3*d;

t1=-0.2; t2=0.7; t3=2.1111;
h2=0.1; h3=0.1;
t4=5.8; t5=5.4; t6=1.2;