Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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Attach their codes, too.

Code:

```
def f(z):
x = real(z)
y = imaginary(z)
return (x^2 + y^2 -1)^3 - x^2*y^3
complex_plot(lambda z: (1/f(z)*i^(z+1)),(-1.5,1.5),(-1.5,1.5),plot_points=300)
```

(The code takes a lot of time to run, for testing purposes run with plot_points=50)

*Last edited by Agnishom (2014-06-07 17:33:31)*

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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I've lost the exact code for this but it is somewhat like this:

POV-Ray Code:

```
#declare e = 2.71828;
#include "textures.inc"
#include "colors.inc"
#include "glass.inc"
camera {
location <0, 0, -10>
look_at <0,0,0>
}
light_source
{
<0,0,-10>
color rgb <1.0, 1.0, 1.0>
shadowless
spotlight
rotate y*clock*-100
}
#declare Ball =
sphere{<0,0,0>,0.08
texture{
pigment{color rgb<1,0.8,0>}
finish {diffuse 0.9 phong 1}
}// end of texture
}// end of sphere
//------------------------------------
#declare X = -5; // start value X
#declare EndX = 5; // end value X
#declare Step = 0.001;// step value
#declare Sine =
union{
#while ( X < EndX + Step)//loop start
object{ Ball translate <X,sin(X),0>}
#declare X = X + Step; // next X
#end // ------------------- loop end
};
#declare X = -5; // start value X
#declare EndX = 5; // end value X
#declare Step = 0.001;// step value
#declare Curvedd =
union{
#while ( X < EndX + Step)//loop start
object{ Ball pigment {color rgb<0,0,1>} translate <X,cos(X)+cos(pow(X,2)),0>}
#declare X = X + Step; // next X
#end // ------------------- loop end
};
#declare X = 0; // start value X
#declare EndX = 6.28; // end value X
#declare Step = 0.001;// step value
#declare Cardioid =
union{
#while ( X < EndX + Step)//loop start
#declare r = 1 - sin(X);
object{ Ball pigment {color rgb<0,1,0>} translate <r*cos(X),r*sin(X),0>}
#declare X = X + Step; // next X
#end}; // ------------------- loop end
#declare X = 0; // start value X
#declare EndX = 6.28; // end value X
#declare Step = 0.001;// step value
#declare Butterfly =
union{
#while ( X < EndX + Step)//loop start
#declare r = pow(e,sin(X)) - 2*cos(4*X) + pow(sin((2*X-pi)/24),5);
object{ Ball texture{Polished_Brass} translate <r*cos(X),r*sin(X),0>}
#declare X = X + Step; // next X
#end}; // ------------------- loop end
#declare X = -6.28; // start value X
#declare EndX = 6.28*2
; // end value X
#declare Step = 0.001;// step value
#declare log_spiral =
union{
#while ( X < EndX + Step)//loop start
#declare b = log(1.61803397)/(3.14159/2);
#declare r = 1*pow(e,b*X);
object{ Ball texture{Gold_Metal} translate <r*cos(X),r*sin(X),0>}
#declare X = X + Step; // next X
#end}; // ------------------- loop end
#declare X = -6.28; // start value X
#declare EndX = 6.28
; // end value X
#declare Step = 0.001;// step value
#declare Fermat_spiral =
union{
#while ( X < EndX + Step)//loop start
#declare r = pow(X,0.5);
object{ Ball texture{Polished_Brass} translate <r*cos(X),r*sin(X),0>}
#declare r = -1*pow(X,0.5);
object{ Ball texture{Polished_Brass} translate <r*cos(X),r*sin(X),0>}
#declare X = X + Step; // next X
#end}; // ------------------- loop end
object {Butterfly texture{Jade}}
/*object {Cardioid}
object {Sine}
object {Curvedd}
object {Fermat_spiral}
object {log_spiral}*/
sphere{ <0,0,0>, 1
texture{T_Glass3
} // end of texture
interior
{I_Glass_Fade_Sqr1}
finish
{F_Glass1}
scale 100
}
```

Uncomment any of the lines in this portion of the code above as you wish:

```
object {Butterfly texture{Jade}}
/*object {Cardioid}
object {Sine}
object {Curvedd}
object {Fermat_spiral}
object {log_spiral}*/
```

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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Mathematica Code:

```
ContourPlot[
Evaluate[Re[
Product[x + I y - (a + I b), {a, -2, 2}, {b, -2, 2}]]], {x, -3,
3}, {y, -3, 3}]
```

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,442

by xslittlegrass.

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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Context Free Code:

```
CF::Size = [s 225]
startshape leggo
shape leggo {
CIRCLE[s 36]
loop 180[r 2]
vein[s .6 hue 65..180 sat .3 b .8 x 12 y 12 ]
loop 206[r 1.75]
myveins[hue 160..250 sat .3 b .7 x -40 y -40] //Comment out
this line for some trippy shizz
loop 20 [r 14..20]
yomama[s .8 hue 0 sat .7 b .7 a -.5 x (-71..-68 )y
(-71..-68)]
mycircle[]
}
shape yomama
rule .99{
CIRCLE[]
yomama[s .995 x -.1...5 y -.1...5 r -10..10]
}
rule .01{
CIRCLE[]
yomama[s .995 x 0...5 y 0 ...5]
yomama[s .6 r -60..60]
}
rule .05{
CIRCLE[]
yomama[s .995 x 0...5 y 0 ...5]
yomama[s .6 r -60..60 a -.8]
}
shape myveins{
vein[]
loop 10 [r 18]
vein[s .2 r -85]
}
shape vein
rule .99{
CIRCLE[a -.2]
vein[s .99 x 0...5 y 0 ...5]
}
rule .0775{
CIRCLE[a -.2]
vein[s .99 x 0...5 y 0 ...5]
vein[s .6 r -60..60]
}
path mycircle{
myrad = 100
MOVETO(0,(-myrad))
ARCTO(0,(myrad),myrad)
ARCTO(0,(-myrad),myrad)
STROKE(1)[]
}
```

by DackAttack

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

'Humanity is still kept intact. It remains within.' -Alokananda

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 84,442

Contributed by: Karl Scherer

**In mathematics, you don't understand things. You just get used to them.I have the result, but I do not yet know how to get it.All physicists, and a good many quite respectable mathematicians are contemptuous about proof.**

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