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Roger Bagula
Works at Bmftg
Attended UCLA
Lives in here in Lakeside
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Roger Bagula
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fractal art (pictures, poems)  - 
 
A pure horned surface:
{Cos[t]/(Sqrt[2] - Cos[p - t]), Cos[p]/(Sqrt[2] - Cos[p - t]),
 Cos[p + t]/(Sqrt[2] - Cos[p - t])}
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Roger Bagula
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fractal art (pictures, poems)  - 
 
perpendicularity / orthogonality technique in the figure eight knot:
I tried a complete “ring-out” solution, but
that doesn’t look at all good.
This solution uses the wavefunction orthogonality (3rd condition)
to tie off two of the ends {xp,zp} and you get a space turn -pike
looking surface!
The yp solved variable has singular “ends” that meet at Infinity.

(* Mathematica*)
(* figure eight knot*)
a = 2; b = 3;
x = (2 + Cos[a*t])Cos[b*t]
y = (2 + Cos[a*t])Sin[b*t]
z = Sin[2*a*t]
w = {x, y, z}
FullSimplify[ExpandAll[w.w]]
Clear[xp, yp, zp, wp]
wp = {xp, yp, zp}
( dot zero :first condition)
w.wp
zp = Cos[4*t]
(* wavefunction orthogonality condition*)
Integrate[
 zp Sin[4 t], {t, -Pi, Pi}]
Solve[xp (2 + Cos[2 t]) Cos[3 t] + yp (2 + Cos[2 t]) Sin[3 t] +
   zp Sin[4 t] == 0, yp]
yp = -((Csc[3 t] (2 xp Cos[3 t] + xp Cos[2 t] Cos[3 t] + Cos[4 t] Sin[4 t]))/(
  2 + Cos[2 t]))

Integrate[y*yp, {t, -Pi, Pi}]
(* 2nd condition Cross product  is constant: checking*)
xp = (2 +
    Sin[2 t]) Sin[3 t]
Integrate[x*xp, {t, -Pi, Pi}]
Simplify[Expand[Cross[w, wp].Cross[w, wp]], Trig -> True]
N[(33905 + 57910 Cos[2 t] + 36635 Cos[4 t] + 17850 Cos[6 t] + 8295 Cos[8 t] +
     4740 Cos[10 t] + 2640 Cos[12 t] + 940 Cos[14 t] + 57 Cos[16 t] -
     138 Cos[18 t] - 91 Cos[20 t] - 22 Cos[22 t] - Cos[24 t] +
     12588 Sin[2 t] + 16480 Sin[4 t] + 11948 Sin[6 t] + 5354 Sin[8 t] +
     1552 Sin[10 t] + 396 Sin[12 t] + 152 Sin[14 t] + 54 Sin[16 t] -
     4 Sin[18 t] - 20 Sin[20 t] - 12 Sin[22 t] -
     2 Sin[24 t])/(32 (2 + Cos[2 t])^2 (1 + 2 Cos[2 t])^2) /. t -> 0]


N[(33905 + 57910 Cos[2 t] + 36635 Cos[4 t] + 17850 Cos[6 t] + 8295 Cos[8 t] +
     4740 Cos[10 t] + 2640 Cos[12 t] + 940 Cos[14 t] + 57 Cos[16 t] -
     138 Cos[18 t] - 91 Cos[20 t] - 22 Cos[22 t] - Cos[24 t] +
     12588 Sin[2 t] + 16480 Sin[4 t] + 11948 Sin[6 t] + 5354 Sin[8 t] +
     1552 Sin[10 t] + 396 Sin[12 t] + 152 Sin[14 t] + 54 Sin[16 t] -
     4 Sin[18 t] - 20 Sin[20 t] - 12 Sin[22 t] -
     2 Sin[24 t])/(32 (2 + Cos[2 t])^2 (1 + 2 Cos[2 t])^2) /. t -> Pi]
Sqrt[%]
Simplify[Expand[w.wp], Trig -> True]
ParametricPlot3D[{N[wp], w}, {t, -Pi + 0.01, Pi - 0.01}]
xa = (8 + Sin[p])xp;
ya = (8 + Sin[p + Pi/4])yp;
za = (8 + Sin[p + 3*Pi/4])*zp;
ww = {xa, ya, za};
gg = Import["EscherSkyandWaterredblueCrop.jpg"]
ParametricPlot3D[N[ww], {t, -Pi + 0.01, Pi - 0.01}, {p, -Pi, Pi},
 Boxed -> False, Axes -> False, Lighting -> "Neutral", PlotPoints -> 200,
 PlotStyle -> {LightBlue, Specularity[White, 10], Texture[gg]},
 TextureCoordinateFunction -> (Normalize[{#1, #2, #3}] &),
 Background -> Black, ImageSize -> 1000, Mesh -> False]
( end)
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Roger Bagula
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Discussion  - 
 
I wish more of his papers were translated into English:
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I did some work on Hausdorff metric between sets.
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Roger Bagula
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Discussion  - 
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Roger Bagula
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fractal art (pictures, poems)  - 
 
My Psuedo-Icosahedron parametric: V=12;F=15;E=25
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Roger Bagula

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Roger Bagula
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2d Julias and Mandelbrots  - 
 
PC4: p[x_]=x + x^2 + 2 x^3 + x^4;
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Roger Bagula
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2d Julias and Mandelbrots  - 
 
Speeding up the unconnected PC7 connects the external islands: here
with a 33rd circle transform:
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Roger Bagula
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2d Julias and Mandelbrots  - 
 
The PC5 and Catalan 5 IFS with a scaling constant and a circle transform:
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Brent W. Hopkins's profile photoRoger Bagula's profile photo
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Already corrected if you clicked on the link...
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Roger Bagula
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fractal art (pictures, poems)  - 
 
My Psuedo-Dodecahedron parametric: V=15;F=12;E=25
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Story
Tagline
inorganic chemist and math type
Introduction

About me? A Natural Philosopher is what they call people like me. I Program computers with Mathematica... I like and do quantum mechanics and cosmology. I have some reviews for Amazon in Mathematics, Physics, fiction and Movies. I'm a big Sci fi movie fan. I've spent the last 30 years as an Fractal activist and am currently a global warming news activist...a "Green". With my groups activity on the web, I have a hobby of paleoarchaeology and the study of mathematical influences on history. I organized my high school reunion 11 years ago and then, didn't go. I write poetry, short stories and fractal based jazz. I still have my draft card. Just got a gift card from the local library as runner up in their poetry contest. Have been making 3d printing models for the last few years.

https://plus.google.com/110803890168343196795/about

http://siggrapharts.ning.com/profile/RogerBagula

http://www.sculpteo.com/en/s/rlbagulatftn/

Old guy who uses Mathematica: started 3d on a Radio Shack color computer in basic about 1979. I'm an Inorganic Chemist by training with physical/ quantum Chemistry. I have been doing fractals since I was using a Commodore 64 for graphics in the 80's. In the 90's I had an Amiga and discovered ray tracing and Phong shading. I'm on a couple of Macs right now and I'm getting old. TFTN was a fractal news letter I published.

http://rogerbagula.brandyourself.com/

Born in National city. Lived childhood mostly in La Mesa, Ca. High School in Lakeside, Ca.1964. Chemistry degree from UCLA 1968. About two years drafted in the Army and 2 semesters graduate school SDSU. Computer programming self taught 1979 on. Fractal newsletter 1993 -2003 and web page design. Number theory work 2002 to present with OEIS entries. Was a Amazon Reviewer / Vine since about 2006. Interest groups at Yahoo, Linked In and Google+ communities. Over 40 years genealogy research since the late 1960's. Researching the Bagula/ Bagola/ Plowka names from Drachhausen, Hochza in Cottbus, Brandenburg,East Germany. I've composed fractal music and done some graphic art with pen and ink and mixed media painting.



Bragging rights
fractalist
Work
Occupation
math programming
Skills
music composition
Employment
  • Bmftg
    math programming, present
Places
Map of the places this user has livedMap of the places this user has livedMap of the places this user has lived
Currently
here in Lakeside
Previously
over there in La Mesa - oakland - redding( oak run) - camp belvoir , virginia - san antonio, texas - los angeles, ( santa monica, lakewood)
Contact Information
Home
Phone
619-5610814
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Address
Lakeside
Roger Bagula's +1's are the things they like, agree with, or want to recommend.
How to use mathematics while playing snooker (For beginners)
science-and-mathematics.blogspot.com

Maths is used in almost every sports. But to say that snooker is a very mathematical game, would be an understatement. For beginners, if you

Sculpteo: 'Möbius_trefoil_Wheel'
www.sculpteo.com

'Möbius_trefoil_Wheel': a featured design of the Sculpteo community

Sculpteo: 'SubDiracC_3'
www.sculpteo.com

'SubDiracC_3': a featured design of the Sculpteo community

Sculpteo: 'Borromean_wheel3'
www.sculpteo.com

'Borromean_wheel3': a featured design of the Sculpteo community

Sculpteo: '5Deltoid_Cage'
www.sculpteo.com

'5Deltoid_Cage': a featured design of the Sculpteo community

Sculpteo: 'Möbius_34torusknot_wheel'
www.sculpteo.com

'Möbius_34torusknot_wheel': a featured design of the Sculpteo community

Lagangian of the Higgs scalar vacuum as a Cauchy -Levy distribution
fractist.blogspot.com

In reviewing Time Reborn by Lee Smolin I realized some thing about the pre-symmetry breaking Higgs vacuum potential.The early universe befor

Einstein's special relativity beyond the speed of light
rspa.royalsocietypublishing.org

Abstract We propose here two new transformations between inertial frames that apply for relative velocities greater than the speed of light,

sci.fractals - Google Groups
groups.google.com

Book review: Survival of the Beautiful By Lucas Brouwers | October 25, 2012 |, Roger Bagula, 7:23 AM. A Math Genius's Sad Calculus Benoit Ma

Sculpteo: 'triaxial_Möbius_22Linked_cylinder2'
www.sculpteo.com

'triaxial_Möbius_22Linked_cylinder2': a featured design of the Sculpteo community

Sculpteo: 'Kluchikov9node'
www.sculpteo.com

'Kluchikov9node': a featured design of the Sculpteo community

Sculpteo: 'Menger_complex_L2'
www.sculpteo.com

'Menger_complex_L2': a featured design of the Sculpteo community

Social psychologists espouse tolerance and diversity: Do they walk the w...
www.sciencedaily.com

Periodically, someone will make the observation that there is a lack of political diversity among psychological scientists; a discussion abo

Sculpteo: 'Dirac_wheel_unitary'
www.sculpteo.com

'Dirac_wheel_unitary': a featured design of the Sculpteo community

Sculpteo: 'teardropKleinbottle'
www.sculpteo.com

'teardropKleinbottle': a featured design of the Sculpteo community

Sculpteo: 'Möbius_21Kleinbottle'
www.sculpteo.com

'Möbius_21Kleinbottle': a featured design of the Sculpteo community

Sculpteo: 'DeltoidKleinbottleD'
www.sculpteo.com

'DeltoidKleinbottleD': a featured design of the Sculpteo community

Sculpteo: 'WhiteheadLinkAsteroid'
www.sculpteo.com

'WhiteheadLinkAsteroid': a featured design of the Sculpteo community

Sculpteo: 'Deltoid_trefoil'
www.sculpteo.com

'Deltoid_trefoil': a featured design of the Sculpteo community