The intricacy of self-similarity

 

Tracing Complexity in Swarm Models

The intriguing aspect of swarm behaviour is the democracy with which the forces react by aggregation and repulsion to one another. This movement is decided in the moment, the same law is for everyone.

In a flock of birds, they are afraid, so they return to themselves, before a new outcome could happen. The behaviour’s simplicity is as a result self-similar and beautiful.

 

 

 

 

 

 

 



 

 

 

 

 

 

EXERCISES IN HIGHER DIMENSION COMPLEXITY OF SWARMS

 

Exercise no. 1: 

My hand, Your Eye Drawings No. 1

 

Source of Idea:

 2D Particle Interactions:

Tracing with Non-Uniform Rational B-splines (NURBS), tracing with fixed geometries:

Exercise no. 2: 

Freehand Drew No. 1 Collective

 

Source of Idea:

 

Jumping between states with multiple interpolations


How do high-dimensional complexity of these models in "x" space create democratic forces? Is there  more room for an individual to have more intuitive behaviour in the swarm, without forsaking the democratic flow?

Jumping between states of differing models of complexity, what do we see?

These exercises are studies in technique of "free-hand" nurb-spline drawings in 2d and 3d planes with a mouse.


Establish The Premise Drawings

 

Profiles of Stationary States:

Tracing States with NURB-splines "free-hand" with the mouse

Rebuilding splines with 5 sets of different outputs in colours: pink, green, red, blue, orange.

Conversion of points along NURBS into point clouds

 

Tracing Swarming Patterns with

 1)  "free hand" where the line of best fit is made with the eye

 2) with given geometries : circles, arcs, etc.

Free hand:        Geometries:

Layering in 3d plane and observing concentric swarm points, where attraction points emerge:

 

Observation No. 1:

The vocal point of the swarm becomes clearly discernible through the replication of the drawing, layered at a distance in a 3d plane

 

 

Modulation Drawings

Variation 1 to 2: Point Cloud Modulation 2d          Variation 3: Point Cloud Modulation 3d                 Variation 4 to 6: Modulation in Perspective            Variation 7 to 9: Surface Creation from Splines      Variation 10 to 12: Surface Projection of splines   Variation 13 to 15: Flatten Elevation                       Variation 16: Sculptured Splines         

Technique is used here with this model, to layer into 3d

 

 

Exercise no. 1: 

My hand, Your Eye Drawing No. 1

 

 

    Hybrid Flat Plane

 

     Intricacy no. 1

         Plane 1

 

         Plane 2

 

 

  

     Intricacy no. 2

 

 

    

    

      Intricacy no. 3

Swarm Hybrid Plane by Tamara Friebel on Sketchfab

"try to find focal points, with your mouse"

   Alive Plane

 

Exercise no. 1: 

My sound, Your ears Piece No. 1

 

 

Intricacy no. 1

Intricacy no. 2

Intricacy no. 3

Exercise no. 2: 

Freehand Drew No. 1 Collective

 

 

Statement for "Freehand Drew No. 1"

The rebuilt curves of the 2 sets of profiles of non-local stochastic models, both the linear diffusion and the non-linear diffusion plots, "enriched" the established nurb splines by offering multiple cloud points, in total five groups, of varying complexity to generate further possibilities for the "hand-eye co-ordination" to selectively choose.

 

These five groups, in colours of red, green, pink, orange and purple were layered in a 3d-plane, according to the observation made in "My hand, your Eye" where the vocal point of the swarm became clearly discernible when the drawing was replicated and layered at a distance on a 3-d plane.