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




Application Architecture

Coded in Flash for easy web browser UI.

Interactive projection calculation performance is very good.

No asynchronous calculations are performed.

Assigned particle symbol, color, shape, roots.

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

Interactive projection calculations are sluggish.

Some asynchronous calculations (e.g. for edges, 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 order 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 manipulation.

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 main window, or simply modify the sliders or number fields for a given locator.

Display particle interaction possibilities based on charge conservation

Clicking a particle highlights the possible particles that it can react with based on the E8 charge conservation. Particle 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 selected 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 “PhysEdge” 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 will display either edges colored by overlap count or particles interactions. Clicks accumulate until the “Clear ClickVerts” is pushed. “ClickAllVerts” auto-clicks all vertices.

Also, using the "Particle Selector – ToE Model” window with “Show more data” checked, the possible interaction particles are displayed below the selected 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 of:

  • Symbols

  • Coordinates

  • MyToE calculated Mass/Lifetimes



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 parameter. The E8Flyer also has a dropdown menu for “Favorite” projections

Coordinate Systems or data sets

Dropdown menu Physics, GUT, and Math Coordinates.

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


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

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

Display Axis Lines

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 lines to be calculated and displayed.

File In(read) / Out(save)

Dropdown menu for saved rotations:preloaded w/Std. Model, Electric Charge, Strong, 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, buttons to select a saved inFile can be used. The “out to file” checkbox activates output (the noAnim8 checkbox is for very large animations that need too much memory to display). The Dir button & file (input field+2digit random#) and type dropdown menu establish output files. 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 particles. Based on their anti-type-color-spin-generation properties, or Group Theory (S0{10},SO(8), E7,F4,G2,A2.

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



View Section:

Perspective view related options..

Particles Size ( pSize)

Some of the particles (currently bosons) are defined with a variable size parameter.


Slider that allows exponential zoom (for non-E8 data sets).


Determines the overall size of the particles in relation to the frame.


Determines the number of ticks per frame.


Determines the range of the X,Y,Z dimension bounding box (frame)


Limit has objects at a vertex outside the frame bounding box displayed at the surface of the bounding box (enabling a “dimensionally rigorous” hyperbolic viewing).

Particle Colors

Color selection slider allows selection from any of 50 MathematicaTM color gradients or Lisi’s original or my new 24 color gradients.Note: pOverlaps overrides the colors.

Frame Center

2D slider to determine preferred location of the frame center (camera points to this)


2D slider to determine preferred camera viewpoint (used for creating animations).

Other display options

Checkboxes for optional displaying of axis, particle vertices, edges, eColorPos, perspective, polygon faces, vertex colors based on pOverlap counts, particle labels, locations, mass-lifetime, physics vs. math vertices. A 0-10 slider to set the nDim Camera location on perspective projections. A 0-5 slider to display “rectifications” of particle locations. A 2-8 slider to alter the number of dims used in edges (for n-cube polytopes).

Number 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 glasses


Select which of 3 (of 6 cubic) face perspectives to display.

Edge / Surface Section:

Display edges related to the selected objects.

Display Edge Lines

Checkbox 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

Checkbox and slider for number of frames and slider for the number of edges per frame. Edges are sorted based on projected edge length.


Checkbox to animate each set of edges based on norm’d length in n-dimensions.


Slider to define the width or radius of edge and triality lines.

Inner Edge Filter

Slider 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

Checkbox selection above main window.

Surface Scaling

A 2D slider determines scaling.

Surface Color

Checkbox to display surfaces in particle colors.


Checkbox to activate the dimension locators in 2D (deactivates particle interactions).

Filter Section:

Filter out sets of particles from the entire list of 256.


Clears all selected filter buttons.

OR / AND Logic

OR or AND logic to 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 & 2), and/or excluded particles.

Anti-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 particles by flying through the 8D space is done by projecting them (dot product) into a 2D or 3D view.

Reset Path

Resets all path settings back to original “Favorite” selection.

t Steps

Time steps slider.

Indicates the number of “movie (or flight) 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.


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.


Radio buttons that select the type of beginning 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 identity dimensions path points.


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.

H,V,Z ptCoord Indicators/Adjustors

For each pair of H,V,Z Dim & Projection vector rows:

  • Toggler Buttons 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.


Lists all 256 particles’ data sorted in sections by Lisi original E8 permutation 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, Fibonacci Sequences and Golden Sections.

Particle Display

Radio buttons for forcing the display (or forcing non-display) of any individual particle.

Best to limit the particles in the main display window by selecting filters, pList=none or MetaFavorite=none 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.

Particle Display

Add button invokes the “forced display” of the selected particle.

Best to limit the particles in the main display window by selecting filters, pList=none or MetaFavorite=none beforehand.

Select “Show more data” to analyze selections against other particle data.

Clear Display

Clear button resets all 256 particles “optional” display property to “?”.

Hadrons (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 Contributed by: Theodore Gray.

Display Elementary Particle Components of Atomic Elements

Click on any atom from any of 4 tabbed detail informational displays (from Wolfram supported data services). This invokes a “forced display” of the lepton/quark components (up to the 4 spin options). This is only useful for Hydrogen or Helium (with optional isotope selector).

Best to limit the particles in the main display window by selecting filters, pList=none or MetaFavorite=none beforehand.