A complete reference for all five healing tools — Fibonacci mathematics, solfeggio frequencies, cymatics, sacred geometry, toroidal field, breathwork and binaural beats.
Overview
The kaleidoscope is a circular canvas divided into mirror-symmetric wedge segments. Coloured rings flow continuously outward from a bright central vanishing point, creating the sensation of travelling through an infinite tunnel. Every number driving the visual — ring spacing, ripple frequency, colour cycling rate, seam oscillation — is derived from the Fibonacci sequence or the golden ratio φ ≈ 1.618.
The audio layer adds nine ancient solfeggio frequencies as pure tones tuned to a 432 Hz foundation, paired with binaural beats or isochronic tones. A breathwork guide, intention setting, session timer, and frequency journey complete a fully structured healing experience.
Rings spawn at the central vanishing point and expand outward continuously, creating the illusion of forward motion through an infinite coloured tube.
The circle is divided into N wedges. Alternate wedges are horizontally flipped before drawing, creating the bilateral symmetry that defines a kaleidoscope.
Hue values are spaced by the golden angle (137.5°), a direct property of φ. No two adjacent rings share a similar hue and no colour ever repeats in a cycle.
Ring boundaries undulate according to a sum of sine waves at Fibonacci frequencies, giving organic, living edges.
The black gaps between segments oscillate at three Fibonacci-spaced frequencies simultaneously, breathing rhythmically rather than staying fixed.
A 432 Hz foundation drone underlies all audio. Solfeggio tones, binaural beats, isochronic pulses, and voice guidance are all layered on top.
Controls Reference
Desktop — move the mouse anywhere on screen and the settings panel slides in automatically from the bottom-right corner. It hides again after 3.5 seconds of mouse inactivity. While typing in any text field the panel stays open until you finish.
Mobile — tap the ⬡ Controls button at the bottom of the screen. The panel slides up full-width from the bottom. Tap outside it, swipe it down, or press Esc to close.
The panel is organised into five collapsible accordion sections: Visual, Audio, Breathwork, Session, and Frequency Journey. Tap any section header to expand or collapse it.
Pause / play animation. Does not fire when typing in a text field.
Toggle fullscreen mode.
Recolour — generates a new random palette.
Close the controls panel.
| Control | Type | What it does |
|---|---|---|
| Preset buttons | 5 buttons | One-tap configurations: Morning Focus, Stress Relief, Sleep Prep, Deep Meditation, Full Journey. Each applies a complete set of visual, audio, breathwork, and session settings simultaneously. A green confirmation message fades in after application. |
| Control | Type | What it does |
|---|---|---|
| Mirrors | Dropdown | Number of symmetric wedge segments. Options follow the Fibonacci sequence: 0 (full circle), 1 (single), 3, 5, 8, 13, 21, 34, 55, 89, 144. At 55+ segments approach a prismatic shimmer. At 0 or 1 there are no seams.Default: 8 |
| Depth | Slider 5–16 | Number of concentric ring layers. Higher values produce denser tunnel geometry.Default: 10 |
| Speed | Slider 1–12 | Tunnel flow rate and global rotation speed. Higher values feel like accelerating.Default: 5 |
| Ripple | Slider 0–20 | Amplitude of the Fibonacci-frequency undulation on each ring's edges. At 0 rings are smooth arcs; at 20 they are highly organic.Default: 8 |
| Seams | Slider 0–5° | Maximum black gap between segments. Oscillates at Fibonacci frequencies up to this ceiling. At 0° segments merge into a seamless pattern.Default: 2.5° |
| Solfeggio | Dropdown | Selects one of nine solfeggio frequencies. Changes the colour palette hue base and cycle rate, and updates audio if running.Default: 528 Hz — Miracle (MI) |
| Low Stimulation | Toggle | Reduces saturation to ~30%, slows animation to 35%, widens seams, simplifies audio to a pure sine wave. For acute stress or sensory sensitivity. |
| Recolour | Button | Generates a new random palette while keeping Fibonacci structural constraints. |
| Pause / Play | Button | Freezes or resumes the animation. Keyboard: Space. |
| Fullscreen | Button | Enters native fullscreen. The canvas scales to fill the screen. Keyboard: F. |
| Save Default | Button | Desktop (Chrome/Edge): picks your kaleidoscope folder once, then writes fibonacci_defaults.js directly — no overwrite prompt. Desktop (Firefox/Safari): downloads fibonacci_defaults.js to replace in your folder. Mobile: saves to localStorage on that device. On next load, settings restore automatically. Distribute all three files together for others to get your exact setup. |
| Reset | Button | Clears localStorage and resets all controls to factory defaults. |
| Control | Type | What it does |
|---|---|---|
| Beat Mode | 3-button toggle | Binaural — left ear hears the solfeggio frequency, right ear hears it plus the beat offset. Brain perceives the difference as an internal pulsation. Requires headphones. Isochronic — the tone is amplitude-modulated at the beat frequency, creating audible pulses. Works over speakers. Blend — both methods at reduced individual volumes. |
| Start / Stop Audio | Button | Initialises the Web Audio engine. Must be pressed after a user gesture due to browser policy. |
| Tone | Slider 0–100 | Volume of the solfeggio tone — fundamental, 2nd harmonic, and sub-octave combined.Default: 60 |
| Beat | Slider 0–100 | Volume of the binaural or isochronic beat layer.Default: 40 |
| Foundation | Slider 0–100 | Volume of the constant 432 Hz foundation drone beneath all other audio.Default: 20 |
| Voice — Gender | Female / Male toggle | Scans the device's available Text-to-Speech voices and selects the best match for the chosen gender. The selected voice name is shown below the toggle. Applies to both breath guide and intention voice. |
| Voice — Softness | Slider 0–100 | Maps to TTS pitch. At 0 the voice speaks at natural pitch; at 100 pitch drops to ~62% of normal, producing a warmer, more resonant, meditative quality.Default: 50 |
| Voice name display | Display | Shows the actual TTS voice in use. Updates when gender is changed. |
| Control | Type | What it does |
|---|---|---|
| Enable breath guide | Toggle | Overlays an expanding and contracting ring on the visual that pulses in sync with the selected pattern. Phase name and countdown appear at a fixed position inside the ring. |
| Pattern | 4-button toggle |
Box 4·4·4·4 — four equal 4-second phases. Calming and balancing. 4·7·8 — 4s inhale, 7s hold, 8s exhale. Activates the parasympathetic nervous system; good for anxiety and sleep. Fibonacci 5·8·5·3 — phases follow Fibonacci ratios. Integrates structurally with the visual mathematics. Coherent 5·5 — 5s in, 5s out. Associated with HRV coherence and stress reduction research. |
| Text size | S / M / L | Size of the phase label and countdown displayed on the canvas.Default: M |
| Voice breath guide | Toggle | Speaks the phase name aloud at each transition using the selected TTS voice and softness setting. Short phrases take priority over intention voice if both are active. |
| Control | Type | What it does |
|---|---|---|
| Duration | 5 / 10 / 20 / 30 min | Length of the timed session.Default: 10 min |
| Start / Stop Session | Button | Starts a countdown visible in the top-right of the canvas. In the final 15 seconds audio fades and the visual dims, ending the session gently. Audio stops automatically at zero. Disabled when a journey is running (journey overrides session). |
| Intention textarea | Text input | Paste any paragraph, affirmation, or list of intentions. The text is split into individual sentences on full stops, exclamation marks, question marks, and line breaks. Each sentence cycles through: 2.2s fade in → 5.5s visible → 2.2s fade out, then the next begins. Editing or pasting new text resets the cycle immediately. |
| Show on visual | Toggle | Displays the fading intention sentences on the canvas above the centre line. Disable to use voice-only without visual text.Default: On |
| Intention text size | S / M / L | Size of the intention text displayed on the canvas.Default: M |
| Voice intention | Toggle | Speaks each sentence aloud as it fades in using the selected TTS voice. |
| Voice speed | Slider 0.60–1.10 | Reading rate for the intention voice specifically. Below 0.60 the voice quality degrades on most platforms.Default: 0.72 |
| Repeat | Dropdown |
Loop continuously — cycles through all sentences indefinitely. Every minute — resets to sentence one at each 60-second boundary, aligning the text with clock time. Once / Twice / 3× / 5× / 10× — plays through all sentences that many full times then stops. Visual and voice both go quiet when the count is reached. |
| Export Session Log | Button | Downloads a plain text file summarising all active settings and elapsed session time, with a blank personal notes section. Named with the current date. Can be kept as a practice record or shared with a therapist. |
| Control | Type | What it does |
|---|---|---|
| Frequency chips | Toggleable buttons | Gold chip buttons for each of the nine solfeggio frequencies. Click any chip to deselect it from the journey; click again to restore. The All button instantly reselects all nine. The journey plays only selected frequencies in ascending order. |
| Mins / step | Slider 1–5 | Minutes spent at each frequency before transitioning to the next. The journey button label shows total duration live: e.g. 9 steps × 2 min = 18 min.Default: 2 |
| ▶ Start / ⏸ Pause | Button | Start begins the journey from the first selected frequency. During the journey it becomes ⏸ Pause — pressing it freezes the visual, mutes audio, and pauses the breathwork guide and countdown. The button then shows ▶ Continue. |
| ↺ Stop & Reset | Button | Stops and resets the journey entirely, restoring audio gain, resuming the visual, and re-enabling the session timer. Only active when a journey is running or paused. |
| Progress bar | Display | A row of step indicators below the buttons. Completed steps are amber, the active step is bright amber, upcoming steps are dim. |
| Journey info | Display | Shows current frequency, step number, and time remaining in the current step. On the canvas, the same info appears faintly at the bottom of the circle throughout the journey. |
Healing Design
A constant subtle oscillator at 432 Hz runs beneath all other audio whenever audio is active. This tuning system is independent of the standard 440 Hz concert pitch and is widely used in sound healing for its perceived warmth and naturalness. The Foundation slider controls its level independently of the solfeggio tones.
Binaural beats require headphones — the two slightly different frequencies must reach each ear independently for the brain to perceive the internal pulsation. Isochronic tones work over speakers because the pulse is built into the amplitude modulation of a single signal. Blend combines both at lower individual volumes. The beat frequency for each solfeggio tone is associated with a specific brainwave band (see the Solfeggio table below).
The breath ring expands during Inhale and contracts during Exhale. The Hold phase after Inhale locks the ring at its maximum radius; the Hold or Rest phase after Exhale locks it at its minimum. The phase name and countdown are anchored at a fixed position inside the visual — they do not track the ring size, so they never fly out of the circle. If Voice breath guide is enabled, the phase name is spoken softly at each transition.
Paste a paragraph, a set of affirmations, or any multi-sentence text. The input splits it at sentence boundaries and cycles through each sentence with a gentle 2.2-second fade in and out, with 5.5 seconds of full visibility. This means a 3-sentence paragraph completes one full pass in about 30 seconds. The Repeat setting controls how many passes occur — Loop for continuous use, or a fixed count. Every minute resets back to the first sentence, which works well when aligned with a session timer.
Both breath guidance and intention reading use the device's built-in Text-to-Speech engine. Gender selection scans available voices by name patterns (Samantha, Karen, Aria → female; Daniel, David, James → male). Softness adjusts the TTS pitch parameter — higher softness produces a warmer, lower-pitched delivery. Voice speed applies only to the intention reading rate, not the breath guide. The breath guide always speaks at the same measured pace regardless of voice speed.
In the final 15 seconds of a timed session, audio fades out gradually and a subtle darkening overlay dims the canvas. This prevents the jarring experience of a session ending abruptly — the experience dissolves gently rather than cutting off.
When enabled: saturation drops to ~30% of normal producing soft, muted pastels; animation speed slows to 35%; seams widen; audio harmonics are removed leaving only a pure fundamental sine wave. Designed for acute stress, sensory sensitivity, or anyone who finds the full experience overwhelming.
The breath ring radius now interpolates smoothly between phases rather than jumping instantly at each boundary. A lerp factor of 9% per frame means the ring glides organically — the visual matches the felt experience of breath, where inhale and exhale blend continuously rather than switching abruptly.
A Presets section sits at the top of the controls panel with five one-tap configurations. Each preset applies a complete set of settings simultaneously — frequency, beat mode, breathwork pattern, speed, low stim mode, session duration, and a suggested intention text. Tap any preset and everything reconfigures instantly.
528 Hz · Binaural · Coherent 5·5 · Speed 6 · 10 min · Intention for the day
396 Hz · Isochronic · 4·7·8 · Speed 3 · Low Stim · 20 min · Releasing tension
174 Hz · Blend · 4·7·8 · Speed 2 · Low Stim · 30 min · Drifting into sleep
528 Hz · Binaural · Box 4·4·4·4 · 13 mirrors · Depth 12 · 20 min
All 9 frequencies · Binaural · Fibonacci breath · 2 min per step · 18 min total
The Kaleidoscope HRV and Toroidal HRV pages support Bluetooth Low Energy (BLE) heart rate monitors via the Web Bluetooth API. Tap 📶 Connect BLE Heart Rate Monitor and select your device from the Chrome device picker.
Chest straps are the recommended sensor. Finger pulse oximeters with a standard BLE GATT profile are also supported:
Chest straps (CooSpo, Magene, Polar H10 etc.) — measure the heart's electrical signal directly, giving highly accurate RR intervals for HRV calculation. These are the preferred option for serious HRV work. SpO₂ is not available from chest straps.
Finger pulse oximeters (BLE-enabled models) — measure heart rate and SpO₂ optically through the fingertip. When the device exposes a standard Pulse Oximeter GATT service, the toolkit will automatically detect and display SpO₂ alongside heart rate.
Tap 📋 Export Session Log at the bottom of the Session section to download a plain text file summarising everything active during your session — solfeggio frequency, beat mode, breathwork pattern, intention text, journey status, voice settings, BPM if biofeedback was running, and elapsed time. A blank personal notes section is included at the bottom.
The file is named with the date (e.g. kaleidoscope-2024-03-15.txt) and can be kept as a therapeutic practice record, shared with a practitioner, or used to reproduce a session that worked particularly well.
528 Hz · Coherent 5·5 breathwork · 10 min session · Intention: your intention for the day
396 Hz · 4·7·8 breathwork · Low Stim on · Isochronic beats · 20 min session
174 Hz · 4·7·8 breathwork · Low Stim on · 30 min session · Voice intention loop
All 9 frequencies · 2 min per step · Fibonacci breathwork · Intention cycling on every minute · No session timer needed — journey is 18 min
Audio Reference
| Freq | Name | Colour | Beat | Brainwave | Association |
|---|---|---|---|---|---|
| 174 Hz | Foundation | Amber | 2 Hz | Delta — deep sleep | Pain relief, grounding |
| 285 Hz | Healing | Yellow-green | 3 Hz | Delta — dreamless rest | Tissue regeneration |
| 396 Hz | Liberation UT | Emerald | 4 Hz | Theta — deep meditation | Release of fear and guilt |
| 417 Hz | Change RE | Cyan | 6 Hz | Theta — creative trance | Facilitating change |
| 528 Hz | Miracle MI | Azure | 8 Hz | Alpha — relaxed focus | DNA repair — reference tone |
| 639 Hz | Connection FA | Violet | 10 Hz | Alpha — calm awareness | Relationships, communication |
| 741 Hz | Intuition SOL | Magenta | 12 Hz | Alpha/Beta — light focus | Awakening intuition |
| 852 Hz | Order LA | Rose | 14 Hz | Beta — active thought | Returning to spiritual order |
| 963 Hz | Divine SI | Full spectrum | 16 Hz | Beta — alert presence | Crown activation |
Mathematics
The Fibonacci sequence F(1, 1, 2, 3, 5, 8, 13, 21…) appears at every level of the visual.
Each ring's normalised radial position is (i / depth + time·speed) mod 1, scaled to canvas radius. When an inner boundary wraps past 1.0 it resets to 0, spawning a new ring at the vanishing point.
k runs over the first three Fibonacci indices, so each ripple layer oscillates at a Fibonacci-multiple of the base frequency — true fractal self-similarity.
Recent Updates
All nine solfeggio frequencies are now aligned to the traditional chakra colour system. Rather than cycling through the full 360° colour wheel, each frequency owns a colour range centred on its chakra hue. The Fibonacci wave function modulates within that range — so colour variation and geometric structure share the same mathematical source.
| Hz | Chakra | Colour centre | Range |
|---|---|---|---|
| 174 | Earth | Deep crimson | ±28° |
| 285 | Earth Star | Magenta-red | ±28° |
| 396 | Root — Muladhara | Red | ±32° |
| 417 | Sacral — Svadhisthana | Orange | ±32° |
| 528 | Solar Plexus — Manipura | Gold | ±36° |
| 639 | Heart — Anahata | Green | ±36° |
| 741 | Throat — Vishuddha | Sky blue | ±30° |
| 852 | Third Eye — Ajna | Indigo | ±28° |
| 963 | Crown — Sahasrara | Violet | ±48° |
The Crown chakra has the widest range (±48°) reflecting its traditional association with the full spectrum of light. A chakra name and description badge appears below the solfeggio selector in both apps, displayed in the chakra's own colour.
A 📌 pin button sits in the top-left of the controls panel header on both apps. When activated (turns purple), the panel stays open permanently on desktop regardless of mouse inactivity. Click again to unpin and restore normal auto-hide behaviour. Useful when fine-tuning settings or during therapeutic sessions where you want controls accessible.
Both apps request a screen wake lock on load, preventing the device display from dimming or turning off during a session. The lock is automatically released when you switch away from the app and re-acquired when you return. Requires iOS 16.4+ or modern Android/Chrome. On unsupported devices the feature silently does nothing.
The S/M/L buttons for breath guide text have been replaced with a continuous slider (range 1–5, default 2.5). This gives finer control over the phase label and countdown size on the canvas.
All voice controls (gender, softness, breath guide voice, intention voice, speed) are hidden on touch/mobile devices and replaced with a quiet note "Voice guidance available on desktop." This is because the default TTS voices on iOS and Android are not suitable for a healing context. On desktop browsers the full voice system is available.
Cymatics — Recent Update
The Cymatics page now offers three rendering styles for each of the nine solfeggio frequency patterns. Organic and Scientific were the original two; Liquid is the new addition.
The wave field modulates colour within the chakra hue range. Background is dark; nodal lines are bright. A gentle angular shimmer moves across the pattern continuously.
Black background with glowing nodal lines in pure chakra colour. Maximum geometric clarity — closest to a photograph of an actual Chladni plate.
Fibonacci turbulence layers perturb the pattern with iridescent, oil-on-water colouring. The geometry is still present but reads as a living fluid surface rather than a static wave field.
Two layers are added on top of the base wave field. The first is a Fibonacci turbulence field: four layers using Fibonacci spatial frequencies (1, 1, 2, 3, 5), with amplitudes decaying by 1/φ per layer and golden-angle phase offsets. The turbulence uses a cos(n·θ) formulation — integer multiples of the toroidal angle — which eliminates the seam artefact that appeared at the atan2 branch cut in earlier versions.
The second layer is iridescent colouring: a Cartesian gradient estimation maps gradient magnitude and angle to a hue shift within the chakra range, simulating the way light refracts off a liquid surface at different angles.
drawImage. This keeps frame rate smooth on mobile while still producing a visually rich result — the upscaling is handled in hardware and the resolution reduction is not perceptible at normal viewing distance.
The glow slider minimum is 5 in Liquid style (vs 10 in other styles). At low glow values the underlying geometric nodal structure becomes more visible through the liquid cell fills, giving control over the geometry-versus-texture balance. At high glow the iridescent fills dominate and the nodal lines become secondary.
The Cymatics patterns are cymatics-inspired — mathematically grounded in the same wave physics that produces real Chladni plate patterns, but rendered as living light rather than sand on a plate. A Chladni plate captures a single static moment; these patterns breathe, rotate, and evolve continuously, closer to what the wave field actually looks like as a living phenomenon. Informed viewers will recognise the connection to real cymatic plate photographs and appreciate the mathematical grounding. The interpretation is honest.
Fifth Tool
The Toroidal Field is the fifth public tool in the For Humanity toolkit. Where the other four tools visualise Fibonacci mathematics projected through light and geometry, the torus page visualises the electromagnetic field geometry of the heart itself.
The heart's electromagnetic field has been measured and mapped by HeartMath Institute researchers. Its geometry is toroidal — energy flows out from the top of the heart, curves around the exterior of the body, and returns through the bottom in a continuous self-sustaining loop. This is not metaphor but measured physical reality: a torus-shaped field extending several feet beyond the body in all directions.
The visualisation renders this as a figure-8 mesh of dipole field lines — the mathematical curves that describe how field lines actually flow around a magnetic dipole. Each line follows the equation r(θ) = L·sin²(θ) in polar coordinates, which is the exact formula for a dipole field line. Multiple lines at different toroidal angles together form the characteristic figure-8 envelope. As coherence increases, more lines appear and the centre convergence point brightens — the field becomes more expansive and more ordered.
HRV coherence — the degree to which the heart rhythm oscillates in a smooth, regular sine wave pattern — correlates with the degree of order in the heart's toroidal field. The 5·5 coherent breathing pattern at 0.1 Hz is the resonant frequency of the heart's toroidal field. Practising coherent breathing at this rate entrains the heart rhythm, increasing coherence and the measured order of the electromagnetic field.
The torus appears at every scale of physical reality. The magnetic field of the Earth is toroidal. Galaxy formation produces toroidal structures. Smoke rings and water vortices are transient tori. At the subatomic level, the electron probability cloud around a nucleus has toroidal modes. In sacred geometry traditions — which predate the physics by millennia — the torus was understood as the fundamental form through which energy sustains itself: the Flower of Life, the Merkaba, and the Sri Yantra all encode toroidal relationships. What modern physics measures as a self-sustaining electromagnetic field, the traditions called the light body or aura. The geometry is the same.
The Pulse speed slider is hard-capped at a maximum rate of 0.006 radians per tick, equivalent to one full field sweep cycle taking a minimum of approximately 8.7 seconds at 60 fps. This keeps the visual well below the 3 Hz flicker threshold associated with photosensitive epilepsy risk. The slow meditative sweep is a feature, not a limitation — it matches the timescale of coherent breathing and feels unhurried.