Sirsty = Spiral of Inverse Radius Space Time.
Firsty = Fabric of Inverse Radius Space Time.

The Sirsty Firsty website is devoted to studying the inverse distance squared law by means of naive marker points rotating in the inverse distance squared field. These naive marker points embody a set of simple harmonic oscillators. The Sirsty Workbench allows you to setup the parameters that shows these points in their simplest form.

These points can be colored by a set of colors in a repeating cycle. This leaves a trail of contrasting color behind as the points move around in their circular paths. The Firsty Workbench allows you to set up the parameters that show these colorful impressions as they are made.

We see that in the inverse distance squared field, the points produce color patterns that are somewhat distorted in comparison to the patterns produced by points rotating in an inverse distance cubed field. The points animated by the inverse distance cubed field produce color patterns that are spaced out at regular intervals.

This suggests the inverse distance cubed field may be the underpinning of the inverse distance squared field. The inverse distance squared field would then be a product or integration of the inverse distance cubed field.

The Sirsty Firsty model shows how a set of simple harmonic oscillators hold points in a formation.

The Sirsty-Firsty model dubs 4 of these patterns Rat, Ape, Monkey, Amphibian.  Each of these patterns appear by a unique configurations of the Firsty workbench.

The Sirsty Workbench

Figure 1. The spiral points workbench is dubbed Sirsty for Spiral of Inverse Radius Space Time. 
The Sirsty workbench employs naive marker points moving at uniform speed in their respective circles.
(Click on image to use workbench)

Table 1. The Sirsty types. Each Sirsty type has a different velocity function V ( R ).
The velocity function determines the speed of each of the many black marker points.
The Sirsty types obey the equation for circular orbital physics that relates velocity V to acceleration a.
Namely, V^ 2 / R = a.

Figure 2. A graph plotting the velocity profiles for the first 8 points in Sirsty types 1 through 5.  
(Click on graph to see full size)

The Firsty Workbench

Figure 3. Firsty stands for Fabric of Inverse Radius Space Time. 
The Firsty workbench employs Sirsty points to lay out colors as the points move step by step around in their respective circles. 
(Click on image to use workbench)

Introducing the Rat Ape Monkey Amphibian designs.

Sirsty 3 & Firsty 1 = SirFir 3-1 designs.

Sirsty 3 is the inverse distance cubed field.
This field has a velocity function of |V| ∝ 1 / R and an acceleration function of |a| ∝ 1 / R^3.

The Firsty 1 designs are made by the spiral arm points moving about in their own orbits. Typically an arm point sits on a single pixel for a number of steps before moving to the next pixel.

Each step looks up a color in the color cycle using a formula that involves the persistence and the size of the color cycle table. The resulting color is painted on the pixel.

Since a point may take many steps to move through a square pixel? The pixel gets painted repeatedly by various colors!

When the arm point finally leaves the next pixel? The last color painted on the pixel remains in place! 

This type of coloring is called Firsty 1 = Fall Step Sampling. Fall as in the color that falls in place based on how many steps the point takes to move entirely through the pixel area.

Figure 4. The Sir Fir (3) (1) pattern dubbed 'Rat'. The five orange circles are the main settings that make this pattern appear.
This particular example was made by setting the Color Cycle to 8 at the start, then going through the numbers back to 1.

Figure 5. The Sir Fir (3) (1) pattern dubbed 'Ape'. The five orange circles are the main settings that make this pattern appear.
The green circle indicates the Ape face.

Figure 6. The Sir Fir (3) (1) pattern dubbed 'Monkey'. The five orange circles are the main settings that make this pattern appear.
The 'Diagonal' setting on the lower right rotates the image by 45 degrees because the Monkey face appears at a 45 degree angle.

Figure 7. The Sir Fir (3) (1) pattern dubbed 'Amphibian'. The five orange circles are the main settings that make this pattern appear.
The 'Horizontal' setting on the lower right rotates the image by 90 degrees because the Amphibian face appears at a 90 degree angle.

Revisiting the Rat Ape Monkey Amphibian designs.

Sirsty 3 & Firsty 2 = SirFir 3-2.

The Firsty 2 designs are similar to Firsty 1 designs.

Firsty 1 coloring keeps whatever color is last painted on a pixel by an arm point moving along its circular path of radius R.

Firsty 2 imposes a rigid minimum increment to the color index that looks up a color in the color cycle table. This is called spring step sampling.

The size of the spring step is determined by the inverse velocity of each point.

Since a point's velocity is a function of the point's radius R, and each point has a unique radius R? Therefor each point has a unique spring step size!

One effect of spring step color sampling is that some arm points (at a certain radius R) have a spring step that looks up the same color in the color cycle table over and over, whatever the step number. These points will then paint out a circle of a single color.

That means Firsty 2 designs can have rings of solid color in them, which Firsty 1 designs do not have.

In Sirsty 3 & Firsty 2 (SirFir 3-2) designs, multiple concentric rings of solid color appear spaced out at regular intervals like target rings.

Figure 8. The Sir Fir (3) (2) pattern dubbed 'Rat'. The five orange circles are the main settings that make this pattern appear.

Figure 9. The Sir Fir (3) (2) pattern dubbed 'Ape'. The five orange circles are the main settings that make this pattern appear.

Figure 10. The Sir Fir (3) (2) pattern dubbed 'Monkey'. The five orange circles are the main settings that make this pattern appear.

Figure 11. The Sir Fir (3) (2) pattern dubbed 'Amphibian'. The five orange circles are the main settings that make this pattern appear.

SirFir Rat / Ape / Monkey / Amphibian Slide Show

(See also Zoo Tour 1 / Tour 2 / Tour 3 )

Sirsty-Firsty (Spiral Arm Color Designs) by Sirsty-Firsty.org
is licensed under a Creative Commons Attribution 4.0 International License.

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