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. This was presented at Generative Art 2023, in Rome, Italy.
Part of P17. Mathematical Tidbits.
- Why the needles images from the second ESA video work: Creating needles with odd n
- An Elementary Multiplication Exercise: Using n,10-Stars to Visualize Last Digit Multiplication Patterns
P10. Sequence Player Chapter. Sequence Player mode, introduced in March 2024, scrolls through all P values where SCF = 1. This produces video sequences showing Waves of Images for any n, S, J values without the “flickering” discussed in E10.2.1. Here are a couple of explainers using Sequence Player. It is worth noting that this mode adjusts to changes in n, S, and J while the sequence is playing but resets to 1 once P = nkS is reached (k is the number of jumps in a jump set). It also resets to the Starting Points P value if that value changes (so an easy way to reset the sequence is to toggle the Starting Points value up and down). The sequence resets to P = 1 if n, S, or J change, even if Starting Points P is not set to 1. Additionally, there are a few images on the 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
- 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: Machines Calculate, but Humans Evaluate, provides a 7-page overview of the Sequence Player mode, presented at Generative Art 2024, in Venice, Italy.
P12. 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 S Varies Unless S is a Multiple of 7
- 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-P-using 7-line generator function Protected
- Multiples of S and the Limits of Image Types
- 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 n between 8 and 25
- Needles with Shields
- G-Line Images given G is Prime
- Composite G-Line Images
P11. 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
- n is divisible by 4: n = 4k Sharpest Central Needles Stars
- n is divisible by 2 but not 4: n = 4k+2, J = 2k-1 Sharpest Central Needles Stars
- Even Sharpest Central Needles with Shields
- Sharpest Central Needles on Sharpest Vertex Frame Stars
- MA. Generalized Sharpest Central Needles