Asier Emuger
In this gallery I tried to simulate some animals, plants or famous characters through a single polynomial equation.
The difficulty lies mainly in two points: firts, imagine the object by means of “easy” forms (when I say “easy” I mean those forms that can be simulated through polynomials of low degree), and second, describe the object mathematically. First point is important because of the limited capacity of the program. Finally, it is also important a proper use of the zoom.
All the images have been done through Surfer2008 or Surfer 1.4.0 Debian package, just with polynomials.
Fórmula
- ((x+1)^2-(y+1)^3)*(a*(x+1)^2-y-0.6)*((9*a*(x+1)^2+(y+1)^2+(z+5)^2-9)) *(9*a*(x+1)^2+y^2+(z+1)^2-9)*(9*a*(x+1)^2+y^2+(z-3)^2-9) *((2*(x+1)^2+(y+1)^2+(z-7)^2-11)) *((z-9)^2+(y+1)^2+(x+2)^2-2) *(((x+1)^2+y)^2+((z-0.9*y-3)*(z-0.9*y+1)*(z-0.9*y+4))^2-0.6) *((z-9)^2+(y+1)^2+x^2-2)*((z-2-(x+1)^2)^2+(y+1)^2-0.01)=0; a=0.62
Insectus Zomorro
Moving the values of parameters Insectus Zomorro can fly and walk!
Surfer2008 (zomorro means insecte in basque)
Fórmula
- c=-0.20, d=5.89, a=0.5, b=0.06 ((y^(2)+5z)^2+((y-0.5-z+(0.1)*d*x^2))^2-0.02*a)*(((y)^2+5z)^2+((y-z+9*c*x^2))^2-a*0.1)* ((x^2+y^2+15*z)^2+((x+y)*(x-y))^2-0.1a)*(2*(x)^2+(y-1.4)^2+3*(z-0.53)^2-3.5)* (2*(x)^2+2*(y)^2+3*(z-0.3)^2-1.4)*(2*(x)^2+2*(y+1)^2+3*(z-0.3)^2-0.7)* (20*(x+0.34)^2+(y+1.4)^2+20*(z-0.2)^2-0.8*a)* (20*(x-0.34)^2+(y+1.4)^2+20*(z-0.2)^2-0.8*a)-b=0
Fórmula
- (35*(x+0.6)^4+(5*y)^4+a*z^4-3.2)*(b*(x+0.8)^6+(5*y)^4+35*z^4-7)* ((x-1.5)^2+8*y^2+8*(z-0.5)^2-0.3)*((x-1.6)^2+8*y^2+8*(z-0.2)^2-0.35)* ((x-1.7)^2+8*y^2+8*(z+0.1)^2-0.4)* ((x-1.6)^2+8*y^2+8*(z+0.4)^2-0.35)*(8*(x-1.2)^2+8*(y-0.16)^2+(z+0.25)^2-0.3)* (8*(x-1.2)^2+(y+0.25)^2+8*(z+0.6)^2-0.3)* (((x-1.7)^2+z^2-1.3)^2+ y^2-c)=0
Fórmula
- (x^2+y^2+z^2-1)*((x^2+y^2)^3-2*a*x^2*y^2*((z-b*4)^3+1))*(x^2+y^2-0.45z)*(x^2+y^2-0.0005)*(z+1)=0
Gatibu loratzen
Moving the parameter the flower grows and flourishes. The title means “flourishing captive” in basque. Surfer2008
Fórmula
- (x^3+y^2+z^2-a*25*x^2)^2 +(y*z*(x-y)*(x-z))^2-3*b=0, a=0.09, b=0.74
Olagarro for Tavira
Olagarro means octopus. Surfer2008
This picture was selected for the Imaginary contest of Tavira:
Fórmula
- ((z-0.5)^2+(x-1)^2+y^2-1) *((z+x-2)^4+(x-y-1)^4+(y+x-1)^4-2)*(0.5*(x+0.8)^2+y^2+(z+1.8)^2-3) *((a*(x+2)^2)+(2*y-2.7)^2+(z+2)^2-1.3)*(a*(x+2)^2+(2*y+2.7)^2+(z+2)^2-1.3) *((b*(x-1)+z+5)^2+y^2+(z+2)^2-1.5)*((-z-0.5-5*y^2)^2+((x+1))^2-c) *((x+3)^2+2*y^2+(z+5)^2-0.2)*(-z-6+d*(x^2+y^2))=0
Txoria txori
Txoria means bird in basque. The title is in the memory of Mikel Laboa:
Fórmula
- (x^2+y^2+0.5*z^2-2)*(((z-1)-x^2)^2+y^2-a) *(((z+0.8)+c*x^2)^2+y^2-b)*((x+0.3)^2+(y+0.6)^2+(z-1.7)^2-0.15)* ((x-0.3)^2+(y+0.6)^2+(z-1.7)^2-0.15)*(0.6*x^2+0.4*(0.8*z+1.4*y+3)^2+(0.7*z+1.5)^2-0.6)* ((z+2+x^2)^2+(y-2-z)^2-d)*((x-0.5)^2+(y+1.3)^2+(z+2.6)^2-0.2)* ((x+0.5)^2+(y+1.3)^2+(z+2.6)^2-0.2)*((x-1.5)^2+0.2*y^2+(z-3.5)^2-0.3)* ((x+1.5)^2+0.2*y^2+(z-3.45)^2-0.3)*((x+2.8)^2+(y+0.1)^2+(z+2.9)^2-0.15)=0
Mr Testis (of kukuxumusu)
This is famous character in Basque Country. The character was made by Kukuxumusu ( http://www. kukuxumusu.com/?___store=english&___from_store=castellano ).
Fórmula
- Formula "Top Secret"
- (x^2+(y-0.6*z)^2+0.5*z^2-2)*(((z-1)-x^2)^2+y^2-a)*(((z+0.9)-0.1*c*(x)^2)^2+(y+0.5-0.5*z)^2-b)*((x+0.3)^2+(y+0.6)^2+(z-1.7)^2-0.15)*((x-0.3)^2+(y+0.6)^2+(z-1.7)^2-0.15)*(0.8*x^2+(0.6*y+1.4)^2+(0.9*z+1.7)^2-0.6)*((z+2.5+x^2)^2+(y-0.8-z)^2-d)*((x-0.5)^2+(y+2.5)^2+(z+2.5)^2-0.2)*((x+0.5)^2+(y+2.5)^2+(z+2.5)^2-0.2)*((x)^3+0.6*(y-x)^3+(z-y-1)^3)=0
Marylin Testis
This is famous character in Basque Country. The character was made by Kukuxumusu ( http://www. kukuxumusu.com/?___store=english&___from_store=castellano ).
Marylin Testis (with paint)
Here I painted (not very well) the image with Paint.
(Yes, I know, it is a trick.)
Fórmula
- Formula "Top Secret"
Fórmula
- (x^2+y^2)*(x^2+(y+1)^2)*(x^2+(y-1)^2)*((x+1)^2+y^2)*((x+1)^2+(y+1)^2)*((x+1)^2+(y-1)^2)* (x^2+z^2)*(x^2+(z+1)^2)*((x+1)^2+z^2)*((x+1)^2+(z+1)^2)*(z^2+y^2)*(z^2+(y+1)^2)*(z^2+(y-1)^2)*((z+1)^2+y^2)*((z+1)^2+(y+1)^2)*((z+1)^2+(y-1)^2)-0.0001*a=0; a=0.06
Fórmula
- ((x^2+y^2-9)^2+z^2-0.1b)*((x+3)^2+y^2+z^2-c)*((x^2+y^2-28.25)^2+z^2-0.1b)*((x+3.5)^2+(y-4)^2+z^2-3b)*((x^2+y^2)* (x^2+z^2)*(z^2+y^2)*((x+y)^2+z^2)*((x+z)^2+y^2)*((y+z)^2+x^2)*((y+z)^2+(x+y)^2)*((y+z)^2+(x+z)^2)*((y+x)^2+(x+z)^2)-a*0.001)=0, b=0.02, a=0.5,
Fórmula
- Error.
Asier Emuger
And this is the author of the gallery. Born in Basque Country in 1986.
The formula is complex, it requires to much power to Surfer and to any program known.
Insectus zomorro (image quality 6000)
Armiarma (image quality 7000)
San Fermin (Image quality 5000)
Olagarro (Image quality 7000)
Txoria txori (image quality 7000)
The author, thinking on integrals.
Fórmula
- 0=((x-1.1)^2+(y-0.5)^2+(z-0.9)^2-0.15)*((x-1.1)^2+(y+0.5)^2+(z-0.9)^2-0.15)*((x-2)^2+12*y^2+(5*z+0.6*x-5)^2-3)*((x-2)^2+12*y^2+(8*z-4.4)^2-3)*((z-0.2)^2+(x-0.6)^2+2*y^2-2)*(0.5*(x+0.8)^2+y^2+(z-0.2*x+1.8)^2-3)*((a*(x+1.3)^2)+(2*y-2.7)^2+(z-0.2*x+1.5)^2-0.8)*(a*(x+1.3)^2+(2*y+2.7)^2+(z-0.2*x+1.5)^2-0.8)*((b*(x-1)-z+0.2)^2+y^2+(z+2)^2-2)*(((-z)-0.5-3*y^2)^2+((x+0.2))^2-c)*(z-0.2*x+4.6)
halcyon
halcyon, endemic bird from Cape Verde.
The picture was requested by cabo verde’s contest.
