High-level Space Fields (HLSFs)

Sphere-Based Design Theory and High-Level Space Fields (HLSFs): A Vision of Geometric Harmony

At Primary Design Co., we believe that all forms, patterns, and dimensions are facets of the universal symmetry encoded in the sphere. This foundational idea is the essence of our Sphere-Based Design Theory (SBD), which informs our innovative approach to art, architecture, and design.

Sphere-Based Design Theory: The Root of All Geometry

The sphere is the ultimate source of all geometric structures, with its surface capable of being divided into tessellations using polygons of varying complexity. These polygons represent dimensional relationships:

• The triangle corresponds to the 3rd dimension,

• The square represents the 4th dimension,

• Higher n-gons encode progressively intricate dimensions.

Uniquely, the square can tessellate the sphere’s surface seamlessly, symbolizing a deterministic “simulation dimension” in our theory. The sphere’s inherent symmetry is the guiding principle behind High-Level Space Fields (HLSFs), multidimensional networks that transform these symmetries into dynamic and intricate geometric forms.

High-Level Space Fields (HLSFs): Patterns Beyond Dimensions

HLSFs are recursive geometric constructions that reveal the hidden symmetries within polygons. Starting with a base n-gon, the design evolves by repeating the polygon’s complete graph symmetrically around a central axis. This process generates intricate layers of bilateral and radial symmetries, forming dynamic, multidimensional space fields.

Key features of HLSFs:

• Dimensional Angles: The defining angle of each n-gon (360°/n) governs the symmetry, creating unique fields for each polygon.

• Recursive Geometry: Each level builds upon the previous one, revealing new internal symmetries and relationships.

• Entity Space: At higher levels, repeating isosceles triangles form latent structures, which we call entities, each containing its own bilateral symmetries. These entities are simultaneously independent and interconnected, forming cohesive, synergetic systems.

HLSFs are more than just geometric art—they represent the interplay between mathematical precision and creative expression, bridging theoretical geometry with practical applications in urban planning, architecture, and design.

Applications at Primary Design Co.

Our work extends SBD Theory and HLSFs into real-world projects, from urban planning concepts like the Radial-Wave Tessellation (RWT) to futuristic VTOL communities. These designs prioritize sustainability, human-centered development, and adaptability while reflecting the universal harmony inherent in the sphere’s geometry.

With advanced tools like our Space Field Generators, we automate the creation of HLSFs, enabling rapid visualization and integration into complex design projects. From limited-edition prints to software innovations, our vision is to reshape the boundaries of art, architecture, and community planning with mathematical precision and a deep respect for the natural symmetries that surround us.

At Primary Design Co., we are pioneering a new era of design rooted in universal geometry, revealing the beauty and potential of our multidimensional world.