Daniel Wilson

A 3,5 spiral lattice with value shifting along the plastochrone ratio.

A 3,5 spiral lattice. The gray line is the ontogenic (ontogenetic) spiral. The blue and yellow lines are the parastichies. The red intersections are labeled along the ontogenic spiral. Numbers increase regularly along the parastichies.

A 4,3 spiral lattice. The gray line is the ontogenic (ontogenetic) spiral. The blue and yellow lines are the parastichies. The red intersections are labeled along the ontogenic spiral. Numbers increase regularly along the parastichies.

A 5,4 spiral lattice. The gray line is the ontogenic (ontogenetic) spiral. The blue and yellow lines are the parastichies. The red intersections are labeled along the ontogenic spiral. Numbers increase regularly along the parastichies.

A 6,5 spiral lattice. The gray line is the ontogenic (ontogenetic) spiral. The blue and yellow lines are the parastichies. The red intersections are labeled along the ontogenic spiral. Numbers increase regularly along the parastichies.

I've been fascinated by the 1989 work of F. Rothen & A.-J. Koch: "Phyllotaxis or the properties of spiral lattices. - II. Packing of circles along logarithmic spirals" but I'm finding the math difficult to follow for the circle packing. I did learn how to create their spiral lattices. #MathArt

Four images showing the process of turning a 3-fold Apollonian gasket into a fantasy map.

Work in progress images.

*Editing and coloring was done in Krita.

Fantasy map based on an Apollonian gasket, made of circular continents and islands, mostly filled with steep mountains and trees. Created over the course of a week using Excel, Krita, pen & paper. "Somewhere in the sea of eternity lies a mystical land with a circular coast and infinite isles, created by a powerful wizard afflicted by genius and madness. The land shapeshifts as one navigates its terrain, serving as haven for the inhabitants, and horror to invaders."

I added snow to the mountains of my 3-fold Apollonian gasket fantasy map. The inked parts like the mountains and forests were scanned in and assembled. The original gasket was created using Excel. Editing, layers and coloring were done in Krita.

#art #worldbuilding #cartography #mathart #ttrpg #dnd

Parametric curves with rainbow gradients.

Variations of radial perturbation of a circle.
#MathArt

Line art for three interlaced knots.

Three interlaced knots edited together. Created in Excel and Krita.

Something I started in 2022 and just got around to finishing.
#MathArt

0 ≤ θ ≤ 20π

Angle table with degrees and radians.

A circle with radius of 2, modulated by two sinusoidal functions, creating a highly symmetric oscillating pattern.

Radial perturbation of a circle. #MathArt #MathSky #ParametricCurve

x = (2 + u + v)cos θ
y = (2 + u + v)sin θ
u = -0.2 sin (0.9θ)
v = 0.4 sin (7.1θ)
0 ≤ θ ≤ 500π/9

A rose curve with coordinates for self-intersections and radii.

Years of practice and study. I think more people are interested in the eye candy than the numbers. But studying the data is where I've gained the most understanding.

Degrees corresponding to crossings (self-intersections).

Rose curves with crossings (self-intersections).

Roulette curve ribbon plots with intersections.

Lengths, coordinates for crossings, & radii.

The best kind! 🧙

I lack the educational background of a mathematician, but I've studied the data behind roulette curves for many years. I have insights. I have equations. I have so many questions. Have I made discoveries and if so what should I do with them?

A graph showing various x & y coordinates on a circle with degree angles and equations each with a radius and an angle in radians. Created in Excel.

Equations and angles for various circle coordinates.

x = r cos θ
y = r sin θ

0 ≤ θ ≤ 2π

A graph showing various x & y coordinates on a circle with degree angles and equations each with a radius and an angle in radians. Created in Excel.

A graph showing various x & y coordinates on circles with degree angles and equations each with a radius and an angle in radians. Created in Excel.

A graph showing various x & y coordinates on circles with degree angles and equations each with a radius and an angle in radians. Created in Excel.

A graph showing various x & y coordinates on circles with degree angles and equations each with a radius and an angle in radians. Created in Excel.

Equations and angles for various circle coordinates.

x = r cos t
y = r sin t

t = 0 to 2π

#RouletteCurve #epicycloid #MathArt #cardioid

#RouletteCurve #epicycloid #MathArt #Ranunculoid

#RouletteCurve #hypocycloid #MathArt #tricuspoid #deltoid

A photo and spreadsheets for a model of personality traits.

Spreadsheets using a fear-based personality model.

#RouletteCurve #mesocycloid #MathArt #pentagram

3 years ago today I had a laptop, external hd and 2 stacks of cds stolen by workers from The Home Depot. I was chronically aspirating liquids during this time of my life and was not in the best mindset to understand what was done to me until 4 months later. It was 100% of my life's work over the span of a decade or more. Thankfully I had about 30% on other computers, enough to continue my work. Besides a lifetime of photos, the most irreplaceable things were my writings and my more off-the-wall projects like story generators and character simulators. The math art has been the easiest to replace and expand upon. Everything I still have from before 6/24/2022 is a miracle to me.

A photo from 2016 of my desk while working on a cube-based personality simulator.

I love MC Escher's work! Have you seen Regolo Bizzi's art? He makes some cool tessellation art too!

I think this could be called a 5-cusped mesocycloid, a pentacuspoid.

Deltoid -- from Wolfram MathWorld A 3-cusped hypocycloid, also called a tricuspoid. The deltoid was first considered by Euler in 1745 in connection with an optical problem. It was also investigated by Steiner in 1856 and is sometimes ...

Awesome! I look forward to seeing your work! I'm glad to inspire! Wolfram has some good inspiration too!

mathworld.wolfram.com/Deltoid.html

mathworld.wolfram.com/Epicycloid.h...
mathworld.wolfram.com/Hypocycloid....

This might be a better representation.

#RouletteCurve #mesocycloid #MathArt

A photo and diagrams of a model of personality traits.

A cube-based model of personality traits responding to fear. Old work of mine from 2016.

A dark green poster with digitally-created two-dimensional knots colored white and green. 2 large patterns and 17 small patterns. The large patterns are each two knots edited together.

Knots created with Excel using trigonometric parameterization and intercept-toggled graphing of two plot lines. Colored and arranged in Micrografx Picture Publisher.
#MathArt

Tiling based on curves of pursuit algorithm with straight lines removed. Created using Excel and Krita.

#MathArt

Since my circles roll neither on the outside (epicycloid) nor inside (hypocycloid) other circles I'm coining the term mesocycloid, "meso" after the Greek prefix for "middle" and "cycloid" from the Greek word meaning "circular." Can I do that? I suppose I did. #RouletteCurve #Mesocycloid #MathArt