While the E8Viewer/E8Flyer combination of tools is more flexible and comprehensive, Lisi's "Elementary Particle Explorer (EPE)" is a better tool for visuali= zing 2D projections of all 240 particles by using the 8 dimensional axis associated with the E8 vertices. The following ta= ble compares / contrasts EPE with the simpler E8Viewer.

Feature

EPE

E8Viewer

Application Architecture

Coded in Flash for easy web browser UI. =

Interactive projection calculation performanc= e is very good.

No asynchronous calculations are performed.

Assigned particle symbol, color, shape, roots= .

The E8Flyer is coded in = Mathematica^TM and delivered using the free Mathematica^TM Notebook Player (.nbp) format (which requires= a rather large installation).

Interactive projection calculations are slugg= ish.

Some asynchronous calculations (e.g. for edge= s, 2D/3D flight paths) can take minutes.

Particle symbol, color, shape, roots are code generated dynamically. This allows the parametric selection/manipulation = in the UI. The “Particle Selector” takes advantage of this in or= der to reference particle(s) based on their symbolic structure.

Vary the (H)orizontal and (V)ertical 2D projection of the 8 vertex coordinates

Pre-select H & V from the 8 dimensions and click-drag in x-y mouse movements corresponding to H & V selections. =

Fast response to 2D projection axis manipulat= ion.

Need to check the “dimLocs” checkbox which turns particles to dots and turns off clickable particles = for PhysEdges. Somewhat slower “click-drag” response time than ECE. Then "Click-drag" any of the 8 H,V,& Z axis “locators” within the ma= in window, or simply modify the sliders or number fields for a given locator= .

Display particle interac= tion possibilities based on charge conservation

Clicking a particle highlights the possible particles that it can react with based on the E8 charge conservation. Par= ticle specific information is shown below the main window.

Clicking a highlighted particle will then show the particle(s) that would emerge in an interaction between the two selec= ted particles. The 3(or 4 including {0,0} photon) = are highlighted in the main window using thick yellow/ green lines.

Particle masses are not considered in these interactions.

Checkbox for “Phys= Edge” selects Physics particle color/shape/size assignments (as opposed to pure= E8 circles/spheres colored by overlap counts). In 2D and without the “= dimLocs” checked, mouse clicks on vertices wi= ll display either edges colored by overlap count or particles interactions. Clicks accumulate until the “Clear ClickVerts<= /span>” is pushed. “ClickAllVerts” auto-c= licks all vertices.

Also, using the "Particle Selector ̵= 1; ToE Model” window with “Show more data&= #8221; checked, the possible interaction particles are displayed below the selec= ted particle.

For any given particle(antiparticle), the sum(difference) of all pairs that make up its E8 charge components is displayed below if the mass of the selected particle is less than the sum(difference) of the pair. Difference pairs can be thought of as Particle-Antiparticle pairs.

Particle Data=

MouseOver particle in main window.

Also shows coordinate detail below the main window.

MouseOver particle in main window.

E8Flyer also has checkboxes for the display o= f:

·         Symbo= ls

·         Coord= inates

·         MyToE calculated Mass/Lifetimes

Refresh

N/A

Button used to force the display to refresh. = This is necessary for certain options that may take some time to calculate.

Selected MetaFavorites

Menu of 5 selected projections.

Save/Delete new projections during the browser session.

Menu of 40+ selected projection MetaFavorites which can set/change any display para= meter. The E8Flyer also has a dropdown menu for “Favorite” projectio= ns

Coordinate Systems or da= ta sets

Dropdown menu Physics, GUT, and Math Coordina= tes.

Dropdown menu for Binary, E8, Physics, Richte= r, Cell600, Cell5, Cell120 (limit 240 vertice), = AuxData, etc..

Rotation

Button for rotating the 2D display with the click-drag mouse movements.

2D display rotation is not used. 3D displays = use native Mathematica^TM rotation and = zoom options (cntrl or alt-click-drag) =

Display Axis Lines<= /o:p>

Checkbox below main window.=

Checkbox above main window.=

Display Triality Lines

Checkbox below main window.=

In = the Edges / Surfaces section, a button-bar of 4 triality= rotation matrices allows sets of triality lin= es to be calculated and displayed.=

File In(read) / Out(save= )

Dropdown menu for saved = rotations:preloaded w/Std. Model, Electric Charge, Str= ong, GraviWeak, E6 Coxeter, = E8 Coxeter.

No permanent files produced.

Similar to ECE, the “plus” in the upper right corner allows the temporary save of selected configuration to= a list of Bookmarks (pre-loaded with MetaFavorites). In addition with Player Pro or Mathematica, b= uttons to select a saved inFile can be used. The = 220;out to file” checkbox activates output (the noAnim8 checkbox is for very large animations that need too much memory to display). The Dir button &a= mp; file (input field+2digit random#) and type dropdown menu establish output fil= es. This also produces a <file>.m to record the configuration changes. =

Point Systems or

Particle Lists(pLists)

Drop down menu for theory sets Std Model, Gorgi-Glashow(SU(5)), Pati-Salam,E6 (SO(10)), E8.

Dropdown menu for selecting subsets of partic= les. Based on their anti-type-color-spin-generation properties, or Group Theor= y (S0{10},SO(8), E7,F4,G2,A2.

In addition to those above, the following is a list of options avail= able in the more complex E8Flyer.

Feature	E8Flyer
View Section:	Perspective view related options..
Par= ticles Size ( pSize)	Some of the particles (currently bosons) are defined with a variable size parameter.
Zoo= m	Slider that allows exponential zoom (for non-= E8 data sets).
pSc= ale	Determines the overall size of the particles = in relation to the frame.
Tic= ks	Determines the number of ticks per frame.
Fra= me	Determines the range of the X,Y,Z dimension bounding box (frame)
Lim= it	Limit has objects at a vertex outside the fra= me bounding box displayed at the surface of the bounding box (enabling a “dimensionally rigorous” hyperbolic viewing).
Par= ticle Colors	Color selection slider allows selection from = any of 50 Mathematica^TM color gradient= s or Lisi’s original or my new 24 color gradients.Note: pOverlaps overrides the colors.
Fra= me Center	2D slider to determine preferred location of = the frame center (camera points to this)
ViewPoint	2D slider to determine preferred camera viewp= oint (used for creating animations).
Oth= er display options	Checkboxes for optional displaying of axis, p= article vertices, edges, eColorPos, perspective, poly= gon faces, vertex colors based on pOverlap counts,= particle labels, locations, mass-lifetime, physics vs. math vertices. A 0-10 slide= r to set the nDim Camera location on perspective projections. A 0-5 slider to display “rectifications” of part= icle locations. A 2-8 slider to alter the number of dims u= sed in edges (for n-cube polytopes).
Num= ber and Style of Dimensions	Radio buttons to select from: · 2D · 3D · 3D Stereo - Thanks to Mark Fisher www.markfisher.net/~mefisher · 3D Anaglyph - You will red/blue stereo glasse= s
Fac= e	Select which of 3 (of 6 cubic) face perspecti= ves to display.
Edge / Surface Section:	Display edges related to the select= ed objects.
Display Edge Lines	Check= box selection above main window.
Edge Selection	Select from a dropdown menu of Norm’d edges {Value, Qty}.
Edge Color	Sliderbar to determine colors based on the projected edge line length.
Anim8 Edge Lines	Check= box and slider for number of frames and slider for the number of edges per fr= ame. Edges are sorted based on projected edge length.
edgeListAnim8	Check= box to animate each set of edges based on norm’d length in n-dimensions.
eRadius=	Slide= r to define the width or radius of edge and triality lines.
Inner Edge Filter	Slide= r to filter out the inner edge lines of convex shapes based on projected vertex positions.
Triality rotations	There are 4 triality rotation matrices. A button-bar of these allows sets of triality lines to be calculated and displayed.
Display Surfaces	Check= box selection above main window.
Sur= face Scaling	A 2D slider determines scaling.
Sur= face Color	Checkbox to display surfaces in particle colo= rs.
dimLocs=	Checkbox to activate the dimension locators i= n 2D (deactivates particle interactions).
Filter Section:	Filter out sets of particles from t= he entire list of 256.
Cle= ar	Clears all selected filter buttons.
OR = / AND Logic	OR or AND logic t= o be applied to the selected binary filters. OR uses button-bars (allows combining of multiple elements of a binary set) AND uses radio buttons (only 1 selection= per binary set)
Row Filter	Filter particle sets (rows in the ToE model) including Leptons, quarks, bosons (1 &am= p; 2), and/or excluded particles.
Ant= i-Type-Color-Spin-Gen Filters	1 or 2 bit binary sets associated with each particle parameter (anti, pType, color, spin,= gen). Each of these sets defines the shape/color/shade/size of every particle.
Flight Path Section:	Viewing the static positions of par= ticles by flying through the 8D space is done by projecting them (dot product) i= nto a 2D or 3D view.
Res= et Path	Resets all path settings back to original “Favorite” selection.
t S= teps	Time steps slider. Indicates the number of “movie (or flig= ht) frames” to generate in an animation. These are selected using the animation slider displayed after “Refresh” button calculations are complete. This can take minutes to hours depending on the number and complexity of each frame.
Tra= nslational/Rotational/Spin3D	Radio buttons to select whether the chosen sliders will calculate an 8D rotational or translational path. Spin3D will simply rotate the 3D image around the Z axis.
Ide= ntity/ptCoords	Radio buttons that select the type of beginni= ng and ending flight path endpoint calculations: · The 3 selected H,V,Z Identity dimensions are applied= to the initial path point. Final path point is the current H,V,Z location indicators below. · The 3 selected ±H,V,= Z ptCoord= coordinate dimension indicators are applied to the initial and final iden= tity dimensions path points.
Fav= orites	Dropdown menu for selecting a growing set of favorite 8D H, V, Z projection vectors. The number of particles (vertices) and triality relationships are displayed to the right.<= o:p>
H,V,Z ptCoord Indicators/Adjustors	For each pair of H,V,Z Dim & Projection v= ector rows: · Toggler Bu= ttons select which of the 8 dimensions can be used in calculating rotational/translational paths and/or surface calculations. · Vertical slider bars and numeric text fields = can be used to adjust the value of the projections and endpoints for paths. <= o:p>

PlotLists:	Lists all 256 particles’ data sorted in sections by Lisi original E8 permut= ation sets. This includes the 16 “excluded” particles comprised of the 8 dimensions+8 anti-dimension particles. These added particles fill out the 8 bit binary coordinate list which then relates it to Pascal’s Triangle, Fibonac= ci Sequences and Golden Sections.
Par= ticle Display	Radio buttons for forcing the display (or for= cing non-display) of any individual particle. Best to limit the particles in the main displ= ay window by selecting filters, pList=3Dnone or = MetaFavorite=3Dnone beforehand.
Particle Selector:	This was created using a modified "Combining Quarks into Hadrons" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/CombiningQuarksIntoHadrons Contributed by: S. M. Blinder.
Par= ticle Display	Add button invokes the “forced display” of the selected particle. Best to limit the particles in the main displ= ay window by selecting filters, pList=3Dnone or = MetaFavorite=3Dnone beforehand. Select “Show more data” to analyze selections against other particle data.
Cle= ar Display	Clear button resets all 256 particles “optional” display property to “?”.
Had= rons (Baryons/Mesons)	Composite Hadron particles (Baryons/Mesons) components can be visualized by using the appropriate tabs. These also will calculate a list (from Wolfram supported data services) of all particles with the same quark content.
Atomic Element Selector:	This window is a modified "Properties of the Elements" from The Wolfram Demonstrations Project http://demonstrations.wolfram.com/PropertiesOfTheElements Contrib= uted by: Theodore Gray.
Dis= play Elementary Particle Components of Atomic Elements	Click on any atom from any of 4 tabbed detail informational displays (from Wolfram supported data services). This invok= es a “forced display” of the lepton/quark components (up to the 4 = spin options). This is only useful for Hydrogen or Helium (with optional isoto= pe selector). Best to limit the particles in the main displ= ay window by selecting filters, pList=3Dnone or = MetaFavorite=3Dnone beforehand.

Feature	EPE	E8Viewer
Application Architecture	Coded in Flash for easy web browser UI. = Interactive projection calculation performanc= e is very good. No asynchronous calculations are performed. Assigned particle symbol, color, shape, roots= .	The E8Flyer is coded in = Mathematica^TM and delivered using the free Mathematica^TM Notebook Player (.nbp) format (which requires= a rather large installation). Interactive projection calculations are slugg= ish. Some asynchronous calculations (e.g. for edge= s, 2D/3D flight paths) can take minutes. Particle symbol, color, shape, roots are code generated dynamically. This allows the parametric selection/manipulation = in the UI. The “Particle Selector” takes advantage of this in or= der to reference particle(s) based on their symbolic structure.
Vary the (H)orizontal and (V)ertical 2D projection of the 8 vertex coordinates	Pre-select H & V from the 8 dimensions and click-drag in x-y mouse movements corresponding to H & V selections. = Fast response to 2D projection axis manipulat= ion.	Need to check the “dimLocs” checkbox which turns particles to dots and turns off clickable particles = for PhysEdges. Somewhat slower “click-drag” response time than ECE. Then "Click-drag" any of the 8 H,V,& Z axis “locators” within the ma= in window, or simply modify the sliders or number fields for a given locator= .
Display particle interac= tion possibilities based on charge conservation	Clicking a particle highlights the possible particles that it can react with based on the E8 charge conservation. Par= ticle specific information is shown below the main window. Clicking a highlighted particle will then show the particle(s) that would emerge in an interaction between the two selec= ted particles. The 3(or 4 including {0,0} photon) = are highlighted in the main window using thick yellow/ green lines. Particle masses are not considered in these interactions.	Checkbox for “Phys= Edge” selects Physics particle color/shape/size assignments (as opposed to pure= E8 circles/spheres colored by overlap counts). In 2D and without the “= dimLocs” checked, mouse clicks on vertices wi= ll display either edges colored by overlap count or particles interactions. Clicks accumulate until the “Clear ClickVerts<= /span>” is pushed. “ClickAllVerts” auto-c= licks all vertices. Also, using the "Particle Selector ̵= 1; ToE Model” window with “Show more data&= #8221; checked, the possible interaction particles are displayed below the selec= ted particle. For any given particle(antiparticle), the sum(difference) of all pairs that make up its E8 charge components is displayed below if the mass of the selected particle is less than the sum(difference) of the pair. Difference pairs can be thought of as Particle-Antiparticle pairs.
Particle Data=	MouseOver particle in main window. Also shows coordinate detail below the main window.	MouseOver particle in main window. E8Flyer also has checkboxes for the display o= f: · Symbo= ls · Coord= inates · MyToE calculated Mass/Lifetimes
Refresh	N/A	Button used to force the display to refresh. = This is necessary for certain options that may take some time to calculate.
Selected MetaFavorites	Menu of 5 selected projections. Save/Delete new projections during the browser session.	Menu of 40+ selected projection MetaFavorites which can set/change any display para= meter. The E8Flyer also has a dropdown menu for “Favorite” projectio= ns
Coordinate Systems or da= ta sets	Dropdown menu Physics, GUT, and Math Coordina= tes.	Dropdown menu for Binary, E8, Physics, Richte= r, Cell600, Cell5, Cell120 (limit 240 vertice), = AuxData, etc..
Rotation	Button for rotating the 2D display with the click-drag mouse movements.	2D display rotation is not used. 3D displays = use native Mathematica^TM rotation and = zoom options (cntrl or alt-click-drag) =
Display Axis Lines<= /o:p>	Checkbox below main window.=	Checkbox above main window.=
Display Triality Lines	Checkbox below main window.=	In = the Edges / Surfaces section, a button-bar of 4 triality= rotation matrices allows sets of triality lin= es to be calculated and displayed.=
File In(read) / Out(save= )	Dropdown menu for saved = rotations:preloaded w/Std. Model, Electric Charge, Str= ong, GraviWeak, E6 Coxeter, = E8 Coxeter. No permanent files produced.	Similar to ECE, the “plus” in the upper right corner allows the temporary save of selected configuration to= a list of Bookmarks (pre-loaded with MetaFavorites). In addition with Player Pro or Mathematica, b= uttons to select a saved inFile can be used. The = 220;out to file” checkbox activates output (the noAnim8 checkbox is for very large animations that need too much memory to display). The Dir button &a= mp; file (input field+2digit random#) and type dropdown menu establish output fil= es. This also produces a <file>.m to record the configuration changes. =
Point Systems or Particle Lists(pLists)	Drop down menu for theory sets Std Model, Gorgi-Glashow(SU(5)), Pati-Salam,E6 (SO(10)), E8.	Dropdown menu for selecting subsets of partic= les. Based on their anti-type-color-spin-generation properties, or Group Theor= y (S0{10},SO(8), E7,F4,G2,A2.