Layer Wall Builder

Watch ordinary integers arrive one at a time. The multiplicative log branch coordinate is the primary view; synchronized linear and frozen-angle panels provide coordinate controls without changing the underlying integers.

PrimeMind · dual-axis control

Build through N

Wall/profile bins A

Selected Ω layer

Block color

Primary X log spread

Dot size

Integer timen = 2

Ready. This is an exploratory construction page; it does not predict primes.

Frozen tree-wall angle + log-height

selected Ω reference · layer-fitted width

Reference view: natural unwrapped circumference from the completed tree angle. The selected layer’s rightmost angle reaches 100%; vertical log height stays globally fixed.

Adjustable-log largest-prime branch + log-height

primary · full log

Primary view: “Full log” gives equal branch ratios equal width. Lower settings continuously relax that spacing toward the synchronized linear control while leaving every integer and vertical height unchanged.

Linear largest-prime branch + log-height

synchronized control · layer-fitted width

Control view: equal largest-prime-factor increments receive equal width. Its rightmost branch in the selected layer reaches 100%, while the data and time remain synchronized with the primary panel.

Selected layer arrival path

J₁ → J₂ → J₃ → …Branch axis

Build the matrix, then hover or click a block to read its complete address.

Bird’s-eye Ω rings

parent → child tree

Radius is Ω(n); angle is the block’s left/right position on its completed tree layer.

Layer-to-layer sequence

ordinary integer order

The path connects consecutive integers as they jump among Ω layers.

Log-height wall profiles

Axis Progress Layers

—

selected-layer integers

—

highest normalized log

—

adjacent-layer correlation

—

best horizontal shift

—

best shifted correlation

Every profile uses the selected shared branch coordinate and the same fixed log-height scale from 0 to 1.

All Ω layer walls · adjustable-log branches

primary · full log · L1 at bottom

The selected log strength changes only horizontal branch spacing. The fixed normalized log-height scale, layers, colors, integer time, and point membership stay synchronized with the linear wall below.

All Ω layer walls · linear largest-prime branches

control · synchronized time · equal integer x-steps

Additive control wall: 2→3 has exactly the same horizontal distance as every other one-integer step. All integers, colors, Ω layers, and log heights are identical to the primary panel above.

Adjustable primary coordinate

uₛ(n)=s·uₗₒg(n)+(1−s)·uₗᵢₙ(n)

LPF(n) is n’s largest prime factor, N is the build limit, and s is the selected log strength: 1, 3/4, 1/2, or 1/4. The blend changes horizontal spacing rather than merely shrinking the plot.

Linear coordinate control

uₗᵢₙ(n)=(LPF(n)−2)/(N−2)

Every possible branch integer receives one equal horizontal step. This tests which apparent curves depend on logarithmic x-spacing.

Frozen-angle reference

uθ(n)=Ω(n)/Ωₘₐₓ · (θ(n)+π)/(2π)

Only the dedicated reference panel uses the completed tree angle, providing a third geometric coordinate control.

Shared log height

z(n)=log(n)/log(N)

Every comparison uses exactly the same vertical scale from 0 to 1; no layer or x-coordinate view is independently stretched.

Construction-driven

The same arithmetic data are shown through three coordinates: an adjustable log-to-linear blend, the pure additive-linear control, and completed-tree angle. A changes profile bin resolution only; it does not change exact point positions.

What survives the controls

Ordering, clump membership, and Ω-layer ancestry are coordinate-independent. Exact slopes, horizontal wavelengths, and apparent compression are coordinate-dependent and must be compared across log strengths and against linear x.