Harmonic Prime Resonance
Harmonic Prime Resonance is a mathematical model within the DragonFire ecosystem that utilizes the unique properties of prime numbers to establish coherent resonance patterns, enabling transformative operations across dimensional spaces through chromatic representation and prime-based harmonics.
Introduction
Harmonic Prime Resonance represents the intersection of number theory, harmonics, and geometric transformation within the DragonFire mathematical architecture. This system establishes prime numbers as fundamental harmonic nodes that create resonance patterns across dimensional spaces.
While GeoMath provides the mathematical operations for geometric transformations and 4D Mathematics handles higher-dimensional number logic, Harmonic Prime Resonance adds a critical layer by mapping the inherent patterns of prime numbers to create a framework for stable transformations between different mathematical domains.
At its core, this model recognizes that prime numbers function as unique "resonant frequencies" in the mathematical landscape. By applying chromatic visualization techniques and harmonic transformations to these primes, the system reveals underlying structures that enable more efficient computation, encryption, and dimensional transmutation.
Core Principle: Harmonic Prime Resonance employs the indivisible nature of prime numbers as fixed reference points in the mathematical universe, using their intrinsic harmony to establish stable transformations between different mathematical spaces and dimensions. Through chromatic visualization and resonance mapping, these prime-based harmonics create coherent patterns that enable novel computational and transformational capabilities.
Key Concepts
Prime Number Foundations
Indivisible mathematical entities that serve as foundational building blocks of natural numbers and create unique patterns when represented visually.
Chromatic Division
Color-based visualization technique that assigns specific colors to numbers based on their mathematical properties, revealing hidden patterns and relationships.
Harmonic Intervals
Mathematical relationships between primes that exhibit resonance properties, creating stable patterns across dimensional spaces.
Prime Clustering
Regions where prime numbers appear in higher density, creating resonance nodes that enable transformational operations.
Dimensional Harmonics
The mapping of prime-based patterns across different dimensional spaces to maintain coherence during transformations.
Resonance Networks
Interconnected systems of prime nodes that establish stable transformational frameworks between mathematical domains.
Prime Color Division
The chromatic visualization of prime numbers and their relationships to composite numbers forms a fundamental aspect of the Harmonic Prime Resonance system:
Chromatic Representation System
The color division system assigns distinct colors to numbers based on their mathematical properties:
// Define color division for numbers
typedef enum {
COLOR_WHITE = 0, // Special case (1)
COLOR_RED, // Prime numbers
COLOR_YELLOW, // Divisible by 2 (even composites)
COLOR_GREEN, // Divisible by 3
COLOR_BLUE, // Divisible by 5
COLOR_PURPLE, // Divisible by 7
COLOR_CYAN, // Divisible by 11
COLOR_ORANGE // Other composites
} number_color_t;
// Determine color for a given number
number_color_t determineNumberColor(uint64_t number) {
// Edge case: 1 is neither prime nor composite
if (number == 1) {
return COLOR_WHITE;
}
// Check if prime using optimized primality test
if (isPrime(number)) {
return COLOR_RED;
}
// Determine divisibility color
if (number % 2 == 0) {
return COLOR_YELLOW;
} else if (number % 3 == 0) {
return COLOR_GREEN;
} else if (number % 5 == 0) {
return COLOR_BLUE;
} else if (number % 7 == 0) {
return COLOR_PURPLE;
} else if (number % 11 == 0) {
return COLOR_CYAN;
}
// Other composites
return COLOR_ORANGE;
}
Visual Pattern Recognition
When natural numbers are arranged and colored according to their properties, distinctive patterns emerge that reveal the underlying mathematical structure:
Color | Mathematical Property | Visual Pattern | Resonance Characteristics |
---|---|---|---|
Red | Prime numbers | Irregular distribution with clustering | Strong harmonic nodes with unique resonance signatures |
Yellow | Even composites | Consistent alternating pattern | Binary oscillation harmonics (2-based resonance) |
Green | Divisible by 3 | Triangular/diagonal patterns | Triadic resonance with 3-fold symmetry |
Blue | Divisible by 5 | Decimal system bands (repeats every 10) | Pentagonal resonance, base-10 anchor points |
Purple | Divisible by 7 | Complex diagonal patterns | Heptagonal resonance, strong geometric coupling |
Chromatic Transformations
The color division system enables complex transformations by mapping color patterns across different mathematical spaces:
// Apply chromatic transformation
void applyToPrimeChromatic(uint64_t* numbers, size_t count,
chromatic_transform_t transform_type) {
// Color map for transformation
number_color_t* color_map = (number_color_t*)malloc(
count * sizeof(number_color_t));
// Determine colors for all numbers
for (size_t i = 0; i < count; i++) {
color_map[i] = determineNumberColor(numbers[i]);
}
// Apply transformation based on type
switch (transform_type) {
case TRANSFORM_PRIME_SHIFT:
applyPrimeShiftTransform(numbers, color_map, count);
break;
case TRANSFORM_RESONANCE_AMPLIFY:
applyResonanceAmplifyTransform(numbers, color_map, count);
break;
case TRANSFORM_HARMONIC_COLLAPSE:
applyHarmonicCollapseTransform(numbers, color_map, count);
break;
case TRANSFORM_DIMENSIONAL_PROMOTE:
applyDimensionalPromoteTransform(numbers, color_map, count);
break;
}
// Free resources
free(color_map);
}
Resonance Patterns
Harmonic Prime Resonance leverages the unique patterns formed by prime numbers to establish stable resonance networks:
Prime Clustering
Regions where prime numbers appear in higher density, creating areas of heightened harmonic resonance:
// Define prime cluster structure
typedef struct {
uint64_t start; // Starting number of cluster
uint64_t end; // Ending number of cluster
uint32_t prime_count; // Number of primes in cluster
double density; // Density of primes in cluster
double resonance_power; // Calculated resonance power
} prime_cluster_t;
// Find prime clusters in number range
prime_cluster_t* findPrimeClusters(uint64_t min, uint64_t max,
double min_density, uint32_t* cluster_count) {
// Initialize cluster array
const uint32_t MAX_CLUSTERS = 1024;
prime_cluster_t* clusters = (prime_cluster_t*)malloc(
MAX_CLUSTERS * sizeof(prime_cluster_t));
*cluster_count = 0;
// Window for density calculation
const uint32_t WINDOW_SIZE = 100;
uint32_t primes_in_window = 0;
// Sliding window to find clusters
for (uint64_t start = min; start <= max - WINDOW_SIZE; start++) {
// Count primes in current window
primes_in_window = 0;
for (uint64_t n = start; n < start + WINDOW_SIZE; n++) {
if (isPrime(n)) {
primes_in_window++;
}
}
// Calculate density
double density = (double)primes_in_window / WINDOW_SIZE;
// If density meets threshold, record cluster
if (density >= min_density && *cluster_count < MAX_CLUSTERS) {
clusters[*cluster_count].start = start;
clusters[*cluster_count].end = start + WINDOW_SIZE - 1;
clusters[*cluster_count].prime_count = primes_in_window;
clusters[*cluster_count].density = density;
// Calculate resonance power based on cluster composition
clusters[*cluster_count].resonance_power =
calculateClusterResonance(start, start + WINDOW_SIZE - 1);
(*cluster_count)++;
}
}
return clusters;
}
Harmonic Intervals
Mathematical relationships between primes that exhibit resonance properties:
// Define harmonic interval types
typedef enum {
INTERVAL_TWIN_PRIME, // Consecutive primes with difference of 2
INTERVAL_COUSIN_PRIME, // Consecutive primes with difference of 4
INTERVAL_SEXY_PRIME, // Consecutive primes with difference of 6
INTERVAL_FIBONACCI, // Prime pairs matching Fibonacci intervals
INTERVAL_PRIME_TRIPLET // Three consecutive primes in close proximity
} harmonic_interval_t;
// Calculate harmonic score for a set of primes
double calculateHarmonicScore(uint64_t* primes, size_t count) {
double score = 0.0;
// Count different harmonic intervals
uint32_t twin_count = 0;
uint32_t cousin_count = 0;
uint32_t sexy_count = 0;
uint32_t fibonacci_count = 0;
uint32_t triplet_count = 0;
// Fibonacci numbers for interval checking
const uint64_t fibonacci[] = {1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144};
const size_t fib_count = sizeof(fibonacci) / sizeof(fibonacci[0]);
// Check for interval patterns
for (size_t i = 0; i < count - 1; i++) {
uint64_t diff = primes[i+1] - primes[i];
// Check for twin primes
if (diff == 2) {
twin_count++;
}
// Check for cousin primes
if (diff == 4) {
cousin_count++;
}
// Check for sexy primes
if (diff == 6) {
sexy_count++;
}
// Check for Fibonacci intervals
for (size_t f = 0; f < fib_count; f++) {
if (diff == fibonacci[f]) {
fibonacci_count++;
break;
}
}
}
// Check for prime triplets
for (size_t i = 0; i < count - 2; i++) {
if (primes[i+2] - primes[i] <= 8) {
triplet_count++;
}
}
// Calculate weighted harmonic score
score = (twin_count * 5.0 +
cousin_count * 3.0 +
sexy_count * 2.5 +
fibonacci_count * 4.0 +
triplet_count * 7.0) / count;
return score;
}
Resonance Networks
Interconnected systems of prime nodes that establish stable transformational frameworks:
// Define resonance network structure
typedef struct {
uint32_t node_count; // Number of nodes in network
prime_node_t* nodes; // Array of prime nodes
uint32_t edge_count; // Number of edges
prime_edge_t* edges; // Array of edges connecting nodes
double network_stability; // Overall network stability
double resonance_magnitude; // Calculated resonance magnitude
} resonance_network_t;
// Build prime resonance network
resonance_network_t* buildResonanceNetwork(uint64_t max_prime,
double connection_threshold) {
// Allocate network structure
resonance_network_t* network = (resonance_network_t*)malloc(
sizeof(resonance_network_t));
// Generate prime list
uint32_t max_nodes = (uint32_t)(max_prime / (log(max_prime) - 1.1));
network->nodes = (prime_node_t*)malloc(max_nodes * sizeof(prime_node_t));
network->node_count = 0;
// Fill node array with primes
for (uint64_t n = 2; n <= max_prime; n++) {
if (isPrime(n)) {
// Create node for this prime
network->nodes[network->node_count].value = n;
network->nodes[network->node_count].connections = 0;
network->nodes[network->node_count].resonance_strength =
calculatePrimeResonance(n);
network->node_count++;
}
}
// Allocate edges (maximum possible edges is n*(n-1)/2)
uint32_t max_edges = network->node_count * (network->node_count - 1) / 2;
network->edges = (prime_edge_t*)malloc(max_edges * sizeof(prime_edge_t));
network->edge_count = 0;
// Create edges between resonant primes
for (uint32_t i = 0; i < network->node_count; i++) {
for (uint32_t j = i + 1; j < network->node_count; j++) {
// Calculate resonance between nodes
double resonance = calculateNodeResonance(
network->nodes[i], network->nodes[j]);
// If resonance meets threshold, create edge
if (resonance >= connection_threshold) {
network->edges[network->edge_count].from = i;
network->edges[network->edge_count].to = j;
network->edges[network->edge_count].strength = resonance;
network->edge_count++;
network->nodes[i].connections++;
network->nodes[j].connections++;
}
}
}
// Calculate network properties
calculateNetworkProperties(network);
return network;
}
Dimensional Mapping
The Harmonic Prime Resonance system establishes mappings between prime-based patterns and higher-dimensional spaces:
Dimensional Representation
Methods for representing prime-based patterns in different dimensional spaces:
// Define dimensional mapping structure
typedef struct {
uint32_t source_dimension; // Source dimension
uint32_t target_dimension; // Target dimension
uint64_t* prime_anchors; // Array of prime anchor points
uint32_t anchor_count; // Number of prime anchor points
transformation_matrix_t matrix; // Transformation matrix
} dimensional_map_t;
// Create dimensional mapping using prime anchors
dimensional_map_t* createDimensionalMap(uint32_t source_dim,
uint32_t target_dim,
uint64_t max_prime) {
// Allocate map structure
dimensional_map_t* map = (dimensional_map_t*)malloc(
sizeof(dimensional_map_t));
map->source_dimension = source_dim;
map->target_dimension = target_dim;
// Determine optimal prime anchors for this mapping
determinePrimeAnchors(map, max_prime);
// Initialize transformation matrix
initTransformationMatrix(&map->matrix, source_dim, target_dim);
// Calculate matrix coefficients based on prime anchors
calculateMatrixFromAnchors(map);
return map;
}
// Map a point between dimensions
void mapPointBetweenDimensions(dimensional_map_t* map,
double* source_point,
double* target_point) {
// Apply transformation matrix to source point
applyTransformationMatrix(&map->matrix, source_point, target_point);
// Apply prime resonance corrections
for (uint32_t i = 0; i < map->anchor_count; i++) {
// Calculate influence of this prime anchor
double influence = calculatePrimeInfluence(
map->prime_anchors[i], source_point, map->source_dimension);
// Apply correction to each target dimension
for (uint32_t d = 0; d < map->target_dimension; d++) {
target_point[d] += influence * getPrimeCorrection(
map->prime_anchors[i], d);
}
}
}
Prime Dimensional Anchors
Prime numbers that serve as stable reference points across dimensional transformations:
// Define prime anchor structure
typedef struct {
uint64_t prime; // Prime number value
uint32_t dimension; // Associated dimension
double resonance_strength; // Anchor resonance strength
uint32_t stability_index; // Anchor stability index
} prime_anchor_t;
// Find optimal prime anchors for a specific dimensional mapping
prime_anchor_t* findOptimalAnchors(uint32_t source_dim,
uint32_t target_dim,
uint32_t count) {
// Allocate anchor array
prime_anchor_t* anchors = (prime_anchor_t*)malloc(
count * sizeof(prime_anchor_t));
// Find special primes for this dimensional transformation
uint64_t max_search = 10000; // Search limit
uint32_t found = 0;
// For each potential prime
for (uint64_t p = 2; p <= max_search && found < count; p++) {
if (isPrime(p)) {
// Calculate dimensional resonance for this prime
double resonance = calculateDimensionalResonance(
p, source_dim, target_dim);
// Calculate stability index
uint32_t stability = calculatePrimeStability(p);
// If resonance is above threshold, add to anchors
if (resonance > 0.7) { // Resonance threshold
anchors[found].prime = p;
anchors[found].dimension =
(resonance > 0.9) ? target_dim : source_dim;
anchors[found].resonance_strength = resonance;
anchors[found].stability_index = stability;
found++;
}
}
}
// Sort anchors by resonance strength
sortAnchorsByResonance(anchors, found);
return anchors;
}
Transdimensional Operations
Mathematical operations that leverage prime resonance patterns to enable stable transformations between dimensions:
// Define transdimensional operation types
typedef enum {
OP_DIMENSION_PROMOTE, // Promote to higher dimension
OP_DIMENSION_DEMOTE, // Demote to lower dimension
OP_DIMENSION_SHIFT, // Lateral shift within dimension
OP_DIMENSION_ROTATE, // Rotate within dimension using prime axis
OP_DIMENSION_MORPH // Morph dimensional representation
} transdim_operation_t;
// Apply transdimensional operation
void applyTransdimensionalOp(void* data, size_t data_size,
transdim_operation_t op_type,
uint32_t source_dim, uint32_t target_dim) {
// Create dimensional map for this operation
dimensional_map_t* map = createDimensionalMap(source_dim, target_dim, 10000);
// Apply operation based on type
switch (op_type) {
case OP_DIMENSION_PROMOTE:
promoteDimension(data, data_size, source_dim, target_dim, map);
break;
case OP_DIMENSION_DEMOTE:
demoteDimension(data, data_size, source_dim, target_dim, map);
break;
case OP_DIMENSION_SHIFT:
shiftDimension(data, data_size, source_dim, map);
break;
case OP_DIMENSION_ROTATE:
rotateDimension(data, data_size, source_dim, map);
break;
case OP_DIMENSION_MORPH:
morphDimension(data, data_size, source_dim, target_dim, map);
break;
}
// Free resources
freeDimensionalMap(map);
}
Implementation Guide
Harmonic Prime Resonance API
The core API provides interfaces for working with prime-based resonance patterns:
// Initialize Harmonic Prime Resonance system
HarmonicPrime* harmonic_prime_init() {
HarmonicPrime* hp = (HarmonicPrime*)malloc(sizeof(HarmonicPrime));
// Initialize subsystems
hp->color_system = initColorSystem();
hp->resonance_system = initResonanceSystem();
hp->dimensional_system = initDimensionalSystem();
// Set default configuration
hp->max_prime = 10000;
hp->default_resolution = PRIME_RESOLUTION_MEDIUM;
hp->default_chromatic_mode = COLOR_MODE_STANDARD;
// Precompute prime table for efficiency
hp->prime_table = buildPrimeTable(hp->max_prime);
return hp;
}
// Build chromatic representation of number range
chromatic_map_t* harmonic_prime_buildChromaticMap(HarmonicPrime* hp,
uint64_t min,
uint64_t max) {
// Validate range
if (min >= max) {
fprintf(stderr, "Error: Invalid range (min must be less than max)\n");
return NULL;
}
// Allocate map structure
chromatic_map_t* map = (chromatic_map_t*)malloc(sizeof(chromatic_map_t));
// Set range
map->min = min;
map->max = max;
map->count = max - min + 1;
// Allocate color array
map->colors = (number_color_t*)malloc(map->count * sizeof(number_color_t));
// Determine color for each number
for (uint64_t n = min; n <= max; n++) {
map->colors[n - min] = determineNumberColor(n);
}
// Calculate map properties
calculateChromaticProperties(map);
return map;
}
// Find prime clusters in number range
prime_cluster_t* harmonic_prime_findClusters(HarmonicPrime* hp,
uint64_t min,
uint64_t max,
double min_density,
uint32_t* cluster_count) {
return findPrimeClusters(min, max, min_density, cluster_count);
}
// Create resonance network
resonance_network_t* harmonic_prime_createResonanceNetwork(HarmonicPrime* hp,
uint64_t max_prime,
double connection_threshold) {
return buildResonanceNetwork(max_prime, connection_threshold);
}
// Create dimensional mapping
dimensional_map_t* harmonic_prime_createDimensionalMap(HarmonicPrime* hp,
uint32_t source_dim,
uint32_t target_dim) {
return createDimensionalMap(source_dim, target_dim, hp->max_prime);
}
// Apply chromatic transformation
void harmonic_prime_applyTransformation(HarmonicPrime* hp,
uint64_t* numbers,
size_t count,
chromatic_transform_t transform_type) {
applyToPrimeChromatic(numbers, count, transform_type);
}
Chromatic Visualization Modes
Different visualization modes for the Harmonic Prime Resonance system:
Visualization Mode | Description | Best For | Example Use |
---|---|---|---|
Standard Chromatic | Basic color division based on prime/composite properties | General pattern visualization, education | Number grid visualization, prime distribution analysis |
Resonance Intensity | Color saturation based on resonance strength | Identifying resonance nodes and patterns | Finding optimal transformation paths, resonance mapping |
Harmonic Spectrum | Continuous color spectrum based on harmonic relationships | Visualizing mathematical harmony, identifying patterns | Complex harmonic analysis, pattern recognition |
Dimensional Mapping | Colors represent dimensional correspondence | Transdimensional operations, dimensional analysis | Data transformation, dimensional shift visualization |
Cluster Emphasis | Highlights prime clusters and emphasizes dense regions | Prime cluster analysis, resonance network mapping | Network optimization, resonance point identification |
// Set chromatic visualization mode
void harmonic_prime_setVisualizationMode(HarmonicPrime* hp,
chromatic_mode_t mode) {
hp->default_chromatic_mode = mode;
// Update color mapping functions based on mode
switch (mode) {
case COLOR_MODE_STANDARD:
hp->color_func = determineStandardColor;
break;
case COLOR_MODE_RESONANCE:
hp->color_func = determineResonanceColor;
break;
case COLOR_MODE_HARMONIC:
hp->color_func = determineHarmonicColor;
break;
case COLOR_MODE_DIMENSIONAL:
hp->color_func = determineDimensionalColor;
break;
case COLOR_MODE_CLUSTER:
hp->color_func = determineClusterColor;
break;
}
}
Performance Optimization
Techniques for optimizing the performance of the Harmonic Prime Resonance system:
- Prime Caching: Precompute prime tables for fast lookups
- Segmented Processing: Process large number ranges in segments
- Resolution Control: Adjust calculation resolution based on need
- Resonance Thresholding: Filter low-resonance connections to reduce complexity
- Optimized Primality Testing: Use efficient algorithms for prime checks
// Optimize Harmonic Prime performance
void optimizeHarmonicPrimePerformance(HarmonicPrime* hp,
optimization_level_t level) {
// Set optimization level
hp->optimization_level = level;
// Configure based on level
switch (level) {
case OPTIMIZATION_MINIMAL:
hp->max_prime = 10000;
hp->use_cache = false;
hp->segment_size = 1000;
hp->connection_threshold = 0.3;
break;
case OPTIMIZATION_BALANCED:
hp->max_prime = 100000;
hp->use_cache = true;
hp->segment_size = 10000;
hp->connection_threshold = 0.5;
break;
case OPTIMIZATION_MAXIMAL:
hp->max_prime = 1000000;
hp->use_cache = true;
hp->segment_size = 100000;
hp->connection_threshold = 0.7;
break;
}
// Initialize or update prime cache
if (hp->use_cache) {
if (hp->prime_table) {
freePrimeTable(hp->prime_table);
}
hp->prime_table = buildPrimeTable(hp->max_prime);
}
// Configure resonance system
configureResonanceSystem(hp->resonance_system,
hp->connection_threshold);
// Configure dimensional system
configureDimensionalSystem(hp->dimensional_system,
hp->optimization_level);
}
Integration with DragonFire Ecosystem
Harmonic Prime Resonance integrates with other DragonFire components to provide prime-based resonance capabilities:
GeoMath Integration
Harmonic Prime Resonance provides harmonic anchors for GeoMath's transformations:
// Integrate Harmonic Prime with GeoMath
void integrateWithGeoMath(HarmonicPrime* hp, GeoMath* gm) {
// Connect Harmonic Prime's resonance system to GeoMath's transformations
hp->geomath = gm;
// Configure prime-based resonance nodes
configurePrimeResonanceNodes(hp, gm);
// Set up prime-based transformation anchors
setupPrimeTransformationAnchors(hp, gm);
// Map chromatic visualization to geometric structures
mapChromaticToGeometric(hp, gm);
// Initialize prime-based harmonic operations
initPrimeHarmonicOperations(hp, gm);
}
4D Mathematics Integration
Harmonic Prime Resonance establishes dimensional mappings for 4D Mathematics:
// Integrate Harmonic Prime with 4D Mathematics
void integrateWith4DMath(HarmonicPrime* hp, FourDMath* math) {
// Connect Harmonic Prime's dimensional system to 4D Math
hp->math_library = math;
// Set up prime-based dimensional anchors
setupPrimeDimensionalAnchors(hp, math);
// Configure transdimensional operations
configureTransdimensionalOperations(hp, math);
// Map resonance patterns to 4D structures
mapResonanceTo4DStructures(hp, math);
// Initialize prime-based 4D operations
initPrime4DOperations(hp, math);
}
DragonHeart Integration
Harmonic Prime Resonance provides resonance patterns for DragonHeart's harmonic processing:
// Integrate Harmonic Prime with DragonHeart
void integrateWithDragonHeart(HarmonicPrime* hp, DragonHeart* heart) {
// Connect Harmonic Prime's resonance patterns to DragonHeart
heart->harmonic_prime = hp;
// Set up prime-based processing modes
setupPrimeProcessingModes(hp, heart);
// Configure resonance-based timing
configurePrimeResonanceTiming(hp, heart);
// Map chromatic visualizations to wave patterns
mapChromaticToWavePatterns(hp, heart);
// Initialize prime-based wave operations
initPrimeWaveOperations(hp, heart);
}
Unified Prime Framework
Harmonic Prime Resonance provides a unified prime-based resonance framework across the DragonFire ecosystem:
Key Integration Insight: Harmonic Prime Resonance serves as a foundational mathematical anchor within the DragonFire ecosystem, providing stable resonance patterns based on the immutable properties of prime numbers. While GeoMath handles geometric transformations and 4D Mathematics enables higher-dimensional operations, Harmonic Prime Resonance ensures that these transformations maintain coherence and stability by leveraging the inherent harmonic properties of primes. This integration creates a mathematical framework where transformations between different spaces and dimensions can occur with minimal loss of information or structural integrity.
Examples
Basic Harmonic Prime Usage
#include "harmonic_prime.h"
int main() {
// Initialize Harmonic Prime Resonance
HarmonicPrime* hp = harmonic_prime_init();
printf("Initialized Harmonic Prime Resonance system\n");
// Build chromatic map for numbers 1-100
chromatic_map_t* map = harmonic_prime_buildChromaticMap(hp, 1, 100);
printf("Built chromatic map for numbers 1-100\n");
printf("Prime count: %d\n", map->prime_count);
// Print prime numbers found
printf("Primes in range: ");
for (uint64_t i = 0; i < map->count; i++) {
if (map->colors[i] == COLOR_RED) {
printf("%lu ", i + map->min);
}
}
printf("\n");
// Find prime clusters
uint32_t cluster_count = 0;
prime_cluster_t* clusters = harmonic_prime_findClusters(
hp, 1, 1000, 0.3, &cluster_count);
printf("Found %d prime clusters in range 1-1000\n", cluster_count);
// Print top 3 clusters by density
printf("Top clusters by density:\n");
for (uint32_t i = 0; i < 3 && i < cluster_count; i++) {
printf("Cluster %d: Range %lu-%lu, Density %.2f, Primes %d\n",
i + 1, clusters[i].start, clusters[i].end,
clusters[i].density, clusters[i].prime_count);
}
// Create resonance network
resonance_network_t* network = harmonic_prime_createResonanceNetwork(
hp, 100, 0.5);
printf("Created resonance network with %d nodes and %d edges\n",
network->node_count, network->edge_count);
printf("Network stability: %.2f\n", network->network_stability);
// Free resources
harmonic_prime_freeResonanceNetwork(hp, network);
harmonic_prime_freeClusters(hp, clusters);
harmonic_prime_freeChromaticMap(hp, map);
harmonic_prime_free(hp);
return 0;
}
Chromatic Transformation Example
// Demonstrate chromatic transformations
void demonstrateChromaticTransformations() {
// Initialize Harmonic Prime Resonance
HarmonicPrime* hp = harmonic_prime_init();
// Create number array
const uint32_t NUM_COUNT = 20;
uint64_t numbers[NUM_COUNT];
// Initialize with consecutive numbers 1-20
for (uint32_t i = 0; i < NUM_COUNT; i++) {
numbers[i] = i + 1;
}
printf("Original numbers:\n");
for (uint32_t i = 0; i < NUM_COUNT; i++) {
printf("%lu ", numbers[i]);
}
printf("\n\n");
// Apply prime shift transformation
harmonic_prime_applyTransformation(hp, numbers, NUM_COUNT,
TRANSFORM_PRIME_SHIFT);
printf("After prime shift transformation:\n");
for (uint32_t i = 0; i < NUM_COUNT; i++) {
printf("%lu ", numbers[i]);
}
printf("\n\n");
// Reset numbers
for (uint32_t i = 0; i < NUM_COUNT; i++) {
numbers[i] = i + 1;
}
// Apply resonance amplify transformation
harmonic_prime_applyTransformation(hp, numbers, NUM_COUNT,
TRANSFORM_RESONANCE_AMPLIFY);
printf("After resonance amplify transformation:\n");
for (uint32_t i = 0; i < NUM_COUNT; i++) {
printf("%lu ", numbers[i]);
}
printf("\n\n");
// Free resources
harmonic_prime_free(hp);
}
Dimensional Mapping Example
// Demonstrate dimensional mapping
void demonstrateDimensionalMapping() {
// Initialize Harmonic Prime Resonance
HarmonicPrime* hp = harmonic_prime_init();
// Create source points in 2D
const uint32_t POINT_COUNT = 5;
double source_points[POINT_COUNT][2] = {
{1.0, 0.0},
{0.0, 1.0},
{-1.0, 0.0},
{0.0, -1.0},
{0.5, 0.5}
};
// Create target arrays for 3D points
double target_points[POINT_COUNT][3];
// Create dimensional map from 2D to 3D
dimensional_map_t* map = harmonic_prime_createDimensionalMap(hp, 2, 3);
printf("Created dimensional map from 2D to 3D\n");
printf("Using %d prime anchors\n", map->anchor_count);
// Map each point from 2D to 3D
for (uint32_t i = 0; i < POINT_COUNT; i++) {
// Map point
mapPointBetweenDimensions(map, source_points[i], target_points[i]);
// Print results
printf("Point %d:\n", i + 1);
printf(" 2D: (%.2f, %.2f)\n",
source_points[i][0], source_points[i][1]);
printf(" 3D: (%.2f, %.2f, %.2f)\n",
target_points[i][0], target_points[i][1], target_points[i][2]);
}
// Free resources
harmonic_prime_freeDimensionalMap(hp, map);
harmonic_prime_free(hp);
}
View more examples in our SDK Examples section or try the Interactive Prime Visualizer Demo.
Next Steps
- Explore the complete Harmonic Prime API Reference
- Download the Harmonic Prime SDK
- Try the Interactive Prime Visualizer Demo
- Learn about GeoMath for harmonic mathematics of space
- Explore 4D Mathematics for higher-dimensional operations