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BUGMAN123.COM
Welcome to my web site. On this site, you will find some of my favorite hobbies and interests, especially science and art. Questions or comments? Please feel free to “bug” me at my email address:MATH ARTWORK
The Hopf map is a special transformation invented by Heinz Hopf that maps to each point on the ordinary 3D sphere from a unique circle of points on the 4D sphere.Taken together, these circles form a fiber bundle called a Hopf Fibration.If you apply a 4D to 3D stereographic projection to the Hopf Fibration, you get a beautiful 3D torus called a Clifford Torus composed of interlinked VillarceauHAND-MADE ARTWORK
Here are some of my drawings, paintings, and other hand-made artwork. Glow-In-The-Dark Rocket, 9/24/16. My son and I made this decorative toy rocket from cardboard rolls and foam that we found in the dumpster. We sprayed it with glow-in-the-dark paint. Tree Airplane - PHYSICS SIMULATIONS AND ARTWORK Here are some physics simulations and artwork along with some Mathematica code. See also my Fluid Motion page. This magnetic field was approximated by a superposition of 2D point sources using the Biot-Savart Law. Click here to download the POV-Ray code for this image. See also my magnetic field representations for a motor, Teslacoil, and
GEAR INVENTIONS AND ARTWORK The ideal profile for a gear tooth is the involute of a circle.The exact shape of the involute curve can be defined by the number of teeth, pitch circle radius, and pressure angle.This animation shows a gear with only 6 teeth, which may not be enough teeth for most applications, but it demonstrates a good example of extreme undercut.Here is some Mathematica code to draw ideal gears: COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles.RENDERED ARTWORK
Here is some of my computer rendered artwork. “Factory” - old version: TrueSpace 3.1, 12/25/97; new version: POV-Ray 3.6.1, 5/21/06. This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive SolidGeometry
BUGMAN123.COM
;*****Useful AutoLisp Functions;*****;Basic Functions (setq 2pi (* 2 pi)) (defun ² (x) (* x x)) (defun tan (x / cosx) (setq cosx (cos x)) (if (/= cosx 0) (/ (sin x HYPERBOLIC GEOMETRY ARTWORK The Poincaré ball is the 3D analogy of the Poincaré disk. It is a projection of uniformly tiled hyperbolic polyhedrons from hyperbolic space into Euclidean space.This projection can be generated by recursively applying spherical inversions to the faces of a sphairahedron (a polyhedron with spherical faces). This is a (12,4) Poincaré ball, meaning that is was generated from a hyperbolic FLUID MOTION SIMULATIONS AND ARTWORK Fluid Motion Simulations and Artwork. Water Ripple Simulation - calculated in Mathematica 4.2, 12/2/04; rendered in POV-Ray 3.6.1, 7/29/05. Here is a simple water ripple simulation showing single slit wave diffraction. The following Mathematica code solves the wave equation with damping using the finite difference method.BUGMAN123.COM
Welcome to my web site. On this site, you will find some of my favorite hobbies and interests, especially science and art. Questions or comments? Please feel free to “bug” me at my email address:MATH ARTWORK
The Hopf map is a special transformation invented by Heinz Hopf that maps to each point on the ordinary 3D sphere from a unique circle of points on the 4D sphere.Taken together, these circles form a fiber bundle called a Hopf Fibration.If you apply a 4D to 3D stereographic projection to the Hopf Fibration, you get a beautiful 3D torus called a Clifford Torus composed of interlinked VillarceauHAND-MADE ARTWORK
Here are some of my drawings, paintings, and other hand-made artwork. Glow-In-The-Dark Rocket, 9/24/16. My son and I made this decorative toy rocket from cardboard rolls and foam that we found in the dumpster. We sprayed it with glow-in-the-dark paint. Tree Airplane - PHYSICS SIMULATIONS AND ARTWORK Here are some physics simulations and artwork along with some Mathematica code. See also my Fluid Motion page. This magnetic field was approximated by a superposition of 2D point sources using the Biot-Savart Law. Click here to download the POV-Ray code for this image. See also my magnetic field representations for a motor, Teslacoil, and
GEAR INVENTIONS AND ARTWORK The ideal profile for a gear tooth is the involute of a circle.The exact shape of the involute curve can be defined by the number of teeth, pitch circle radius, and pressure angle.This animation shows a gear with only 6 teeth, which may not be enough teeth for most applications, but it demonstrates a good example of extreme undercut.Here is some Mathematica code to draw ideal gears: COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles.RENDERED ARTWORK
Here is some of my computer rendered artwork. “Factory” - old version: TrueSpace 3.1, 12/25/97; new version: POV-Ray 3.6.1, 5/21/06. This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive SolidGeometry
BUGMAN123.COM
;*****Useful AutoLisp Functions;*****;Basic Functions (setq 2pi (* 2 pi)) (defun ² (x) (* x x)) (defun tan (x / cosx) (setq cosx (cos x)) (if (/= cosx 0) (/ (sin x HYPERBOLIC GEOMETRY ARTWORK The Poincaré ball is the 3D analogy of the Poincaré disk. It is a projection of uniformly tiled hyperbolic polyhedrons from hyperbolic space into Euclidean space.This projection can be generated by recursively applying spherical inversions to the faces of a sphairahedron (a polyhedron with spherical faces). This is a (12,4) Poincaré ball, meaning that is was generated from a hyperbolic FLUID MOTION SIMULATIONS AND ARTWORK Fluid Motion Simulations and Artwork. Water Ripple Simulation - calculated in Mathematica 4.2, 12/2/04; rendered in POV-Ray 3.6.1, 7/29/05. Here is a simple water ripple simulation showing single slit wave diffraction. The following Mathematica code solves the wave equation with damping using the finite difference method. COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles.PHYSICS EXPERIMENTS
Here is a picture of me working with liquid helium which has a boiling temperature of 4.2 K (-452.1° F.). This was a fun experiment to study the lambda point of liquid helium and the superconducting properties of tin. The lowest temperature we reached was about 1.2 K (-457.2° F.). Piezoelectric Motor Tester -RENDERED ARTWORK
This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive Solid Geometry (CSG) to program scenes. The illusion of lights was created using small discs in front of the camera, similar to Nathan Kopp’s lens flare include file.LINKS
Halloween Holothurians - beautiful sea cucumber with fractal branches. Blue Dragon Sea Slug - looks like an alien creature, see also the Lettuce Sea Slug. Sea Gooseberry - beautiful jellyfish with rainbow colored pulsating lights. Benthic Ctenophore - beautiful jellyfish that looks like lightning. Electric File Clam. MINIMAL SURFACES ARTWORK You can purchase this as a poster, a tie, or a printed fabric pattern. The Gyroid is a type of triply periodic minimal surface that was discovered by Alan Schoen in 1970. It can be approximated by a simple isosurface defined by cos(x)sin(y) + cos(y)sin(z) + cos(z)sin(x) = 0. The surface patterns in this image are actually artifacts that were created as a result of lowering the max_gradientCOIN COLLECTION
Coin Links 1933 Gold Double Eagle - 1933 Gold Double Eagle - world's most valuable coin, sold for $7.5 million in 2002 The Lydian Lion - world's oldest coin, 600 BC Turkey - world's oldest coin, 600 BCTurkey
TESLA - BUGMAN123.COM A Tesla coil is a high voltage transformer with an air core. The primary and secondary coils each have inductance and capacitance so they function as an LC circuit with its own resonant frequency. The primary capacitance comes from a capacitor that discharges across the PAPER MONEY COLLECTION Paper Money Collection Shown 50% scale (36 dpi) United States. 2Dollar Bill - 1976
POTENTIAL FLOW
Potential Flow. A potential flow is characterized by any flow where the velocity is irrotational. Here are some useful formulas for potential flow: Here is a summary of some basic flows used in potential flow calculations: Vortex Outside Cylinder. Vortex Outside Cylinder. Matlab code: gamma=1; a=1; Z=1+1i; POINCARÉ HYPERBOLIC DISK CONFORMAL MAPPING RECIPE Poincaré Hyperbolic Disk Conformal Mapping Recipe. This page explains how to create an interesting design from the Poincaré hyperbolic disk using only conformal mappings (angle preserving transformations). We begin with the (6, 4) Poincaré hyperbolic disk, meaning that each tile has n = 6 sides and m = 4 tiles meeting at each vertex. TheBUGMAN123.COM
Welcome to my web site. On this site, you will find some of my favorite hobbies and interests, especially science and art. Questions or comments? Please feel free to “bug” me at my email address:MATH ARTWORK
The Hopf map is a special transformation invented by Heinz Hopf that maps to each point on the ordinary 3D sphere from a unique circle of points on the 4D sphere.Taken together, these circles form a fiber bundle called a Hopf Fibration.If you apply a 4D to 3D stereographic projection to the Hopf Fibration, you get a beautiful 3D torus called a Clifford Torus composed of interlinked VillarceauHAND-MADE ARTWORK
Here are some of my drawings, paintings, and other hand-made artwork. Glow-In-The-Dark Rocket, 9/24/16. My son and I made this decorative toy rocket from cardboard rolls and foam that we found in the dumpster. We sprayed it with glow-in-the-dark paint. Tree Airplane - PHYSICS SIMULATIONS AND ARTWORK Here are some physics simulations and artwork along with some Mathematica code. See also my Fluid Motion page. This magnetic field was approximated by a superposition of 2D point sources using the Biot-Savart Law. Click here to download the POV-Ray code for this image. See also my magnetic field representations for a motor, Teslacoil, and
COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles. GEAR INVENTIONS AND ARTWORK The ideal profile for a gear tooth is the involute of a circle.The exact shape of the involute curve can be defined by the number of teeth, pitch circle radius, and pressure angle.This animation shows a gear with only 6 teeth, which may not be enough teeth for most applications, but it demonstrates a good example of extreme undercut.Here is some Mathematica code to draw ideal gears:RENDERED ARTWORK
Here is some of my computer rendered artwork. “Factory” - old version: TrueSpace 3.1, 12/25/97; new version: POV-Ray 3.6.1, 5/21/06. This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive SolidGeometry
HYPERBOLIC GEOMETRY ARTWORK The Poincaré ball is the 3D analogy of the Poincaré disk. It is a projection of uniformly tiled hyperbolic polyhedrons from hyperbolic space into Euclidean space.This projection can be generated by recursively applying spherical inversions to the faces of a sphairahedron (a polyhedron with spherical faces). This is a (12,4) Poincaré ball, meaning that is was generated from a hyperbolicBUGMAN123.COM
;*****Useful AutoLisp Functions;*****;Basic Functions (setq 2pi (* 2 pi)) (defun ² (x) (* x x)) (defun tan (x / cosx) (setq cosx (cos x)) (if (/= cosx 0) (/ (sin x FLUID MOTION SIMULATIONS AND ARTWORK Fluid Motion Simulations and Artwork. Water Ripple Simulation - calculated in Mathematica 4.2, 12/2/04; rendered in POV-Ray 3.6.1, 7/29/05. Here is a simple water ripple simulation showing single slit wave diffraction. The following Mathematica code solves the wave equation with damping using the finite difference method.BUGMAN123.COM
Welcome to my web site. On this site, you will find some of my favorite hobbies and interests, especially science and art. Questions or comments? Please feel free to “bug” me at my email address:MATH ARTWORK
The Hopf map is a special transformation invented by Heinz Hopf that maps to each point on the ordinary 3D sphere from a unique circle of points on the 4D sphere.Taken together, these circles form a fiber bundle called a Hopf Fibration.If you apply a 4D to 3D stereographic projection to the Hopf Fibration, you get a beautiful 3D torus called a Clifford Torus composed of interlinked VillarceauHAND-MADE ARTWORK
Here are some of my drawings, paintings, and other hand-made artwork. Glow-In-The-Dark Rocket, 9/24/16. My son and I made this decorative toy rocket from cardboard rolls and foam that we found in the dumpster. We sprayed it with glow-in-the-dark paint. Tree Airplane - PHYSICS SIMULATIONS AND ARTWORK Here are some physics simulations and artwork along with some Mathematica code. See also my Fluid Motion page. This magnetic field was approximated by a superposition of 2D point sources using the Biot-Savart Law. Click here to download the POV-Ray code for this image. See also my magnetic field representations for a motor, Teslacoil, and
COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles. GEAR INVENTIONS AND ARTWORK The ideal profile for a gear tooth is the involute of a circle.The exact shape of the involute curve can be defined by the number of teeth, pitch circle radius, and pressure angle.This animation shows a gear with only 6 teeth, which may not be enough teeth for most applications, but it demonstrates a good example of extreme undercut.Here is some Mathematica code to draw ideal gears:RENDERED ARTWORK
Here is some of my computer rendered artwork. “Factory” - old version: TrueSpace 3.1, 12/25/97; new version: POV-Ray 3.6.1, 5/21/06. This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive SolidGeometry
HYPERBOLIC GEOMETRY ARTWORK The Poincaré ball is the 3D analogy of the Poincaré disk. It is a projection of uniformly tiled hyperbolic polyhedrons from hyperbolic space into Euclidean space.This projection can be generated by recursively applying spherical inversions to the faces of a sphairahedron (a polyhedron with spherical faces). This is a (12,4) Poincaré ball, meaning that is was generated from a hyperbolicBUGMAN123.COM
;*****Useful AutoLisp Functions;*****;Basic Functions (setq 2pi (* 2 pi)) (defun ² (x) (* x x)) (defun tan (x / cosx) (setq cosx (cos x)) (if (/= cosx 0) (/ (sin x FLUID MOTION SIMULATIONS AND ARTWORK Fluid Motion Simulations and Artwork. Water Ripple Simulation - calculated in Mathematica 4.2, 12/2/04; rendered in POV-Ray 3.6.1, 7/29/05. Here is a simple water ripple simulation showing single slit wave diffraction. The following Mathematica code solves the wave equation with damping using the finite difference method. COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles.PHYSICS EXPERIMENTS
Here is a picture of me working with liquid helium which has a boiling temperature of 4.2 K (-452.1° F.). This was a fun experiment to study the lambda point of liquid helium and the superconducting properties of tin. The lowest temperature we reached was about 1.2 K (-457.2° F.). Piezoelectric Motor Tester -RENDERED ARTWORK
This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive Solid Geometry (CSG) to program scenes. The illusion of lights was created using small discs in front of the camera, similar to Nathan Kopp’s lens flare include file.LINKS
Halloween Holothurians - beautiful sea cucumber with fractal branches. Blue Dragon Sea Slug - looks like an alien creature, see also the Lettuce Sea Slug. Sea Gooseberry - beautiful jellyfish with rainbow colored pulsating lights. Benthic Ctenophore - beautiful jellyfish that looks like lightning. Electric File Clam. MINIMAL SURFACES ARTWORK You can purchase this as a poster, a tie, or a printed fabric pattern. The Gyroid is a type of triply periodic minimal surface that was discovered by Alan Schoen in 1970. It can be approximated by a simple isosurface defined by cos(x)sin(y) + cos(y)sin(z) + cos(z)sin(x) = 0. The surface patterns in this image are actually artifacts that were created as a result of lowering the max_gradientCOIN COLLECTION
Coin Links 1933 Gold Double Eagle - 1933 Gold Double Eagle - world's most valuable coin, sold for $7.5 million in 2002 The Lydian Lion - world's oldest coin, 600 BC Turkey - world's oldest coin, 600 BCTurkey
TESLA - BUGMAN123.COM A Tesla coil is a high voltage transformer with an air core. The primary and secondary coils each have inductance and capacitance so they function as an LC circuit with its own resonant frequency. The primary capacitance comes from a capacitor that discharges across the PAPER MONEY COLLECTION Paper Money Collection Shown 50% scale (36 dpi) United States. 2Dollar Bill - 1976
POTENTIAL FLOW
Potential Flow. A potential flow is characterized by any flow where the velocity is irrotational. Here are some useful formulas for potential flow: Here is a summary of some basic flows used in potential flow calculations: Vortex Outside Cylinder. Vortex Outside Cylinder. Matlab code: gamma=1; a=1; Z=1+1i; POINCARÉ HYPERBOLIC DISK CONFORMAL MAPPING RECIPE Poincaré Hyperbolic Disk Conformal Mapping Recipe. This page explains how to create an interesting design from the Poincaré hyperbolic disk using only conformal mappings (angle preserving transformations). We begin with the (6, 4) Poincaré hyperbolic disk, meaning that each tile has n = 6 sides and m = 4 tiles meeting at each vertex. TheBUGMAN123.COM
Welcome to my web site. On this site, you will find some of my favorite hobbies and interests, especially science and art. Questions or comments? Please feel free to “bug” me at my email address:MATH ARTWORK
The Hopf map is a special transformation invented by Heinz Hopf that maps to each point on the ordinary 3D sphere from a unique circle of points on the 4D sphere.Taken together, these circles form a fiber bundle called a Hopf Fibration.If you apply a 4D to 3D stereographic projection to the Hopf Fibration, you get a beautiful 3D torus called a Clifford Torus composed of interlinked VillarceauHAND-MADE ARTWORK
Here are some of my drawings, paintings, and other hand-made artwork. Glow-In-The-Dark Rocket, 9/24/16. My son and I made this decorative toy rocket from cardboard rolls and foam that we found in the dumpster. We sprayed it with glow-in-the-dark paint. Tree Airplane - PHYSICS SIMULATIONS AND ARTWORK Here are some physics simulations and artwork along with some Mathematica code. See also my Fluid Motion page. This magnetic field was approximated by a superposition of 2D point sources using the Biot-Savart Law. Click here to download the POV-Ray code for this image. See also my magnetic field representations for a motor, Teslacoil, and
COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles. GEAR INVENTIONS AND ARTWORK The ideal profile for a gear tooth is the involute of a circle.The exact shape of the involute curve can be defined by the number of teeth, pitch circle radius, and pressure angle.This animation shows a gear with only 6 teeth, which may not be enough teeth for most applications, but it demonstrates a good example of extreme undercut.Here is some Mathematica code to draw ideal gears:RENDERED ARTWORK
Here is some of my computer rendered artwork. “Factory” - old version: TrueSpace 3.1, 12/25/97; new version: POV-Ray 3.6.1, 5/21/06. This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive SolidGeometry
HYPERBOLIC GEOMETRY ARTWORK The Poincaré ball is the 3D analogy of the Poincaré disk. It is a projection of uniformly tiled hyperbolic polyhedrons from hyperbolic space into Euclidean space.This projection can be generated by recursively applying spherical inversions to the faces of a sphairahedron (a polyhedron with spherical faces). This is a (12,4) Poincaré ball, meaning that is was generated from a hyperbolicBUGMAN123.COM
;*****Useful AutoLisp Functions;*****;Basic Functions (setq 2pi (* 2 pi)) (defun ² (x) (* x x)) (defun tan (x / cosx) (setq cosx (cos x)) (if (/= cosx 0) (/ (sin x FLUID MOTION SIMULATIONS AND ARTWORK Fluid Motion Simulations and Artwork. Water Ripple Simulation - calculated in Mathematica 4.2, 12/2/04; rendered in POV-Ray 3.6.1, 7/29/05. Here is a simple water ripple simulation showing single slit wave diffraction. The following Mathematica code solves the wave equation with damping using the finite difference method.BUGMAN123.COM
Welcome to my web site. On this site, you will find some of my favorite hobbies and interests, especially science and art. Questions or comments? Please feel free to “bug” me at my email address:MATH ARTWORK
The Hopf map is a special transformation invented by Heinz Hopf that maps to each point on the ordinary 3D sphere from a unique circle of points on the 4D sphere.Taken together, these circles form a fiber bundle called a Hopf Fibration.If you apply a 4D to 3D stereographic projection to the Hopf Fibration, you get a beautiful 3D torus called a Clifford Torus composed of interlinked VillarceauHAND-MADE ARTWORK
Here are some of my drawings, paintings, and other hand-made artwork. Glow-In-The-Dark Rocket, 9/24/16. My son and I made this decorative toy rocket from cardboard rolls and foam that we found in the dumpster. We sprayed it with glow-in-the-dark paint. Tree Airplane - PHYSICS SIMULATIONS AND ARTWORK Here are some physics simulations and artwork along with some Mathematica code. See also my Fluid Motion page. This magnetic field was approximated by a superposition of 2D point sources using the Biot-Savart Law. Click here to download the POV-Ray code for this image. See also my magnetic field representations for a motor, Teslacoil, and
COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles. GEAR INVENTIONS AND ARTWORK The ideal profile for a gear tooth is the involute of a circle.The exact shape of the involute curve can be defined by the number of teeth, pitch circle radius, and pressure angle.This animation shows a gear with only 6 teeth, which may not be enough teeth for most applications, but it demonstrates a good example of extreme undercut.Here is some Mathematica code to draw ideal gears:RENDERED ARTWORK
Here is some of my computer rendered artwork. “Factory” - old version: TrueSpace 3.1, 12/25/97; new version: POV-Ray 3.6.1, 5/21/06. This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive SolidGeometry
HYPERBOLIC GEOMETRY ARTWORK The Poincaré ball is the 3D analogy of the Poincaré disk. It is a projection of uniformly tiled hyperbolic polyhedrons from hyperbolic space into Euclidean space.This projection can be generated by recursively applying spherical inversions to the faces of a sphairahedron (a polyhedron with spherical faces). This is a (12,4) Poincaré ball, meaning that is was generated from a hyperbolicBUGMAN123.COM
;*****Useful AutoLisp Functions;*****;Basic Functions (setq 2pi (* 2 pi)) (defun ² (x) (* x x)) (defun tan (x / cosx) (setq cosx (cos x)) (if (/= cosx 0) (/ (sin x FLUID MOTION SIMULATIONS AND ARTWORK Fluid Motion Simulations and Artwork. Water Ripple Simulation - calculated in Mathematica 4.2, 12/2/04; rendered in POV-Ray 3.6.1, 7/29/05. Here is a simple water ripple simulation showing single slit wave diffraction. The following Mathematica code solves the wave equation with damping using the finite difference method. COMPUTER PROGRAMMING Here is some Mathematica code to demonstrate 3D graphics. A perspective projection is applied to the triangles and Phong shading is used to interpolate the surface normals across each triangle. The simplest method is the Painter’s Algorithm which draws all the polygons in the order they overlap. However, this does not account for intersecting triangles.PHYSICS EXPERIMENTS
Here is a picture of me working with liquid helium which has a boiling temperature of 4.2 K (-452.1° F.). This was a fun experiment to study the lambda point of liquid helium and the superconducting properties of tin. The lowest temperature we reached was about 1.2 K (-457.2° F.). Piezoelectric Motor Tester -RENDERED ARTWORK
This design is based on my old 1989 “Factory” drawing. POV-Ray (Persistence of Vision Ray Tracer) is a free ray tracing program that uses a Scene Description Language (SDL) with Constructive Solid Geometry (CSG) to program scenes. The illusion of lights was created using small discs in front of the camera, similar to Nathan Kopp’s lens flare include file.LINKS
Halloween Holothurians - beautiful sea cucumber with fractal branches. Blue Dragon Sea Slug - looks like an alien creature, see also the Lettuce Sea Slug. Sea Gooseberry - beautiful jellyfish with rainbow colored pulsating lights. Benthic Ctenophore - beautiful jellyfish that looks like lightning. Electric File Clam. MINIMAL SURFACES ARTWORK You can purchase this as a poster, a tie, or a printed fabric pattern. The Gyroid is a type of triply periodic minimal surface that was discovered by Alan Schoen in 1970. It can be approximated by a simple isosurface defined by cos(x)sin(y) + cos(y)sin(z) + cos(z)sin(x) = 0. The surface patterns in this image are actually artifacts that were created as a result of lowering the max_gradientCOIN COLLECTION
Coin Links 1933 Gold Double Eagle - 1933 Gold Double Eagle - world's most valuable coin, sold for $7.5 million in 2002 The Lydian Lion - world's oldest coin, 600 BC Turkey - world's oldest coin, 600 BCTurkey
TESLA - BUGMAN123.COM A Tesla coil is a high voltage transformer with an air core. The primary and secondary coils each have inductance and capacitance so they function as an LC circuit with its own resonant frequency. The primary capacitance comes from a capacitor that discharges across the PAPER MONEY COLLECTION Paper Money Collection Shown 50% scale (36 dpi) United States. 2Dollar Bill - 1976
POTENTIAL FLOW
Potential Flow. A potential flow is characterized by any flow where the velocity is irrotational. Here are some useful formulas for potential flow: Here is a summary of some basic flows used in potential flow calculations: Vortex Outside Cylinder. Vortex Outside Cylinder. Matlab code: gamma=1; a=1; Z=1+1i; POINCARÉ HYPERBOLIC DISK CONFORMAL MAPPING RECIPE Poincaré Hyperbolic Disk Conformal Mapping Recipe. This page explains how to create an interesting design from the Poincaré hyperbolic disk using only conformal mappings (angle preserving transformations). We begin with the (6, 4) Poincaré hyperbolic disk, meaning that each tile has n = 6 sides and m = 4 tiles meeting at each vertex. TheCONTENTS
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