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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 97,132

by xslittlegrass.

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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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'

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 97,132

Contributed by: Karl Scherer

**In mathematics, you don't understand things. You just get used to them.**

**If it ain't broke, fix it until it is.**

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Happy New Year!

```
TreeGraph[RandomInteger[#] \[DirectedEdge] # + 1 & /@ Range[0, 2013],
VertexSize -> Table[i -> RandomReal[10], {i, 2013}],
VertexStyle ->
Table[i -> ColorData["CherryTones"] /@ RandomReal[1, 1], {i, 2013}],
EdgeStyle -> RGBColor[0.3, 1, 0.5], ImageSize -> Full,
Background -> Black, GraphLayout -> "RadialEmbedding",
EdgeShapeFunction ->
GraphElementData[{"HalfFilledArrow", "ArrowSize" -> .005}],
PlotLabel -> Style["a tree with 2015 nodes", Gray, 20]]
```

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

**David****Member**- From: Notbumpkinland
- Registered: 2014-04-23
- Posts: 2,707

Wow, that one looks interesting.

Bravo Agnishom!

Let brotherly love continue.

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Thanks

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

'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

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