Modular Reduction Projection Explorer

Modulus Configuration

Modulus M 32

Manual Input (2-10000)

Animation Controls

Animation Mode

Frame Delay (ms) 500

Speed Multiplier 1.0×

Animation Range

Loop Animation

Display Options

Projection Lines

Channel Rings

Show All Ring Points

Invert Mode (Inner↔Outer)

Point Color Mode

Farey Line Color Mode

Farey Line Thickness 1.0

Constellation Highlight

Filter Residues

Multi-Modulus View

Enable Multi-Modulus Mode

Modulus Range

Multi-Mod Point Coloring

Multi-Mod Ring Coloring

Show r-to-r Connections

Gap Connections (2n) 2

Show Gap Connections (r to r+2n)

Connection Color Mode

Connection Thickness 0.5

Connection Opacity 50%

Ring Spacing 1.0

Labeling Options

Show Point Labels

Label All Rings

Label Mode

Label Size (px) 12

Label Distance 1.25

Label Coprimes Only

Label Every Nth Point (Outer Ring)

Label Every Nth Point (Inner Rings)

View Controls

Theme

Canvas Background

Custom Background Color

Ring Color Mode

Custom Ring Color

Zoom 1.00×

Global Rotation 0°

Per-Ring Rotation 0.0°

Per-Ring Rotation (Manual)

Line Thickness 1.00

Point Size 6.0px

Opacity 100%

Statistics

Modulus M	32
φ(M)	16
Coprime	16
Non-coprime	16
Channels	6
Density	50.0%
Class	Composite

ω(M)=1

Analysis

Show Detailed Analysis

Color Key

Cyan = Irreducible (gcd=1)

Red = Reducible (gcd>1)

Red Lines = Farey Channels

Blue = Outer ring (M circle)

Farey Lines: Connect each reducible residue r/M on the outer ring to its reduced form r'/M' on the corresponding inner channel ring.

Channel Angles (2πr/M)

Show Channel Details

Show Angle Overlay on Rings

Angle Display Format

Data Export

Export Resolution (px)

Include Legend

Include Title & Analysis