These materials have been created after Electronic String Art was completed. They assume familiarity with the material in **ESA** and simply push the material in different directions. When appropriate, these explainers will reference **ESA** sections using the shorthand such as the E10.2.1 noted below, but link to the preliminary version of this section in **PwP**.

Generative Art: Erfle, Generative Art 2023, provides a 10-page overview of electronic string art.

**Mathematical Tidbits.**

- Why the needles images from the second
**ESA**video work: Creating needles with odd**n** - An Elementary Multiplication Exercise: Using
,10-Stars to Visualize Last Digit Multiplication Patterns**n**

*Sequence Player *Chapter* . Sequence Player *mode, introduced in March 2024, scrolls through all

*values where SCF = 1. This produces video sequences showing*

**P***Waves of Images*for any

*,*

**n***,*

**S***values without the “flickering” discussed in E10.2.1. Here are a couple of explainers using*

**J***Sequence Player*. It is worth noting that this mode adjusts to changes in

*,*

**n***, and*

**S***while the sequence is playing but resets to 1 once*

**J***=*

**P***is reached (*

**nkS***is the number of jumps in a jump set). It also resets to the*

**k***Starting Points*value if that value changes (so an easy way to reset the sequence is to toggle the

**P***Starting Points*value up and down). The sequence resets to

*= 1 if*

**P***,*

**n***, or*

**S***change, even if*

**J***Starting Points*

**is not set to 1. Additionally, there are a few images on the**

*P**Picked Sequences*page that provide even easier entertainment just by touching the image.

- Two forms of dynamism: The Ticking Clock examines drawing an individual image; A Beating Clock focuses on sequences of images.
- How Many Images are in a
*Sequence Player*Sequence? This is an extension of E18.5.- An alternative analysis: Fractional Analysis of Full Density Images

- This explainer provides a new take on 6,2-stars: Intertwined 6,2-Stars.
- Additionally, here are challenge questions based on this image: 6,2-Star Challenge Questions

- Truncated Stars and Stars with Eyelets
- On the Relative Size of Polygons and Stars in Jump Set Vertex Frames
- Challenge Question: An Initial Counting Squares Question with Hints

- The Ultimate
*Zig-Zag*Image- Challenge Question: Counting Squares in the
*Zig-Zag*VF

- Challenge Question: Counting Squares in the
- About
*Zig-Zag*Corkscrews and Weaves - Kicking the Tires of an Image Sequence
- Challenge Question: CQ for Extended Zig-Zag Squares Image given Horizontal and Vertical Diameters
- Challenge Question: CQ Sharpest Right Triangles with 4 sets of lines

- Using a Square to Create an Ultimate Triangular Zig-Zag Image Sequence
- Challenge Question: CQ Triangular Corkscrews and Weaves

- Taking a Static Image out for a
*Sequence Player*Ride - Comparing SCF > 1 Images to nearby SCF = 1 Images

Generative Art: ErfleGA2024, provides an 8-page overview of the *Sequence Player* mode.

**Generalizing 3SST Chapter. **This material is an outgrowth of trying to understand *Three Shape-Shifting Triangles* in a more systematic fashion.

- An Introduction to Analyzing 7-Line
*Single-Step*Images *Cracked Open*and*Overly Closed*Images- The Same Subdivisions Dots are used to Create Irregular
*Single-Cycle*7-gons and 7-grams - Different Images Arise as
Varies Unless*S*is a Multiple of 7**S** - Variations on
*Small Images* *Single-Cycle*Images use the same Subdivision Dots as*k*Varies*The 7-Line Generator Function*version of the*String Art Excel*file- An
*Excel*file for this chapter: Post-ESA String-Art-with--using 7-line generator function Protected*P*

- An
- Multiples of
and the Limits of Image Types*S* - Variations on
*Polygons and Stars in a Cycle* - Four Sets of
*Single-Cycle*7-line Images Beyond 7-Point Stars - A Balancing Act: 3SST Revisited
- A Typology of 7-Line Base Images for
between 8 and 25*n* - Needles with Shields
-Line Images given**G**is Prime**G**- Composite
-Line Images*G*

**Even Sharpest Central Needles Stars.** This is an outgrowth of an open question posed in E11.7.

- An Introduction to Even Sharpest Central Needles Stars
is divisible by 4:**n**= 4**n**Sharpest Central Needles Stars**k**is divisible by 2 but not 4:**n**= 4**n**+2,**k**= 2**J**-1 Sharpest Central Needles Stars**k**- Even Sharpest Central Needles with Shields
- Sharpest Central Needles on Sharpest Vertex Frame Stars
**MA.**Generalized Sharpest Central Needles