Collections
This is Series 1 of VisualMathArt. The series visualises the Collatz Conjecture and the Fractal Tree algorithm. Each line segment width, length, angle and intensity has been drawn with a degree of randomness. No graphics editor has been used. The line path has been determined by the algorithm. I hope you derive pleasure and inspiration from the first series and what mathematics can visualise.
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This is Series 2 of VisualMathArt. The series visualises the Sierpiński Triangle and the T-Square (Fractal Square) algorithm. Each line segment width, length, angle, and intensity has been drawn with various iterations and some images contain up to 3.5 million squares/triangles. No graphics editor has been used. The line path has been determined by the algorithm. I hope you derive pleasure and inspiration from the second series and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Ethereum OpenSea @VisualMathArt
This is Series 3 of VisualMathArt. The series illustrates two Fractal Patterns, one starting with three lines and the second with six lines starting from the middle. Each line splits into two lines in each iteration. Each line segment width, length, angle, and intensity is drawn slightly differently in each iteration. No graphics editor has been used. The line path has been determined by the algorithm. I hope you derive pleasure and inspiration from the third series and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
This is Series 5 of VisualMathArt. The series visualises the landscape elevation and particle reaction to a Vector field. Both are generated using Perlin Noise. Each point and particle is coloured and moves according to the intensity of a field and the random changes in elevation. No graphics editor has been used. The elevation points and particle path has been determined by the algorithm. I hope you derive pleasure and inspiration from the fifth series and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
This is Series 6 of VisualMathArt. The series visualises the Hilbert curve in various orders of n. When n = 1 a line is drawn, connecting the four points in a u-shaped "Hilbert line". If n is increased, three new neighbouring Hilbert lines are added to each existing Hilbert line, resulting in four quadrants, each with a u-shaped Hilbert line. The top-right and the top-left quadrants are rotated and the first and last points in the Hilbert line are connected to the points in the neighbouring Hilbert lines. This fractal shape is called the Hilbert curve, which is a continuous line connecting all the points in the image. Some of the illustrations in this collection contain a Hilbert curve connecting up to 4.2 million points. The points and the line path have been determined by the algorithm. No graphics editor has been used. I hope you derive pleasure and inspiration from the sixth series and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
This is Series 7 of VisualMathArt. The series visualises Circle packing. The circles are randomly placed, and with no overlap. If a circle is too small, it will increase in size until it reaches its closest neighbour. Some of the images in this collection contain up to 10,000 circles with random colours and sizes. No graphics editor has been used. I hope you derive pleasure and inspiration from the seventh series and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
This is Series 8 of VisualMathArt. The series visualises the Random Walk. A point is placed. From there, a new point is randomly located and a line is drawn between the points. From the latest point, a line is drawn to a new point close by. This process is then repeated, and a path is created and coloured randomly, varying in thickness and intensity. Some of the images in this collection contain up to 7.5 million lines with random colours and sizes. No graphics editor has been used. I hope you derive pleasure and inspiration from Series 8 and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
This is Series 9 of VisualMathArt. The series visualises the Apollonian gasket. The fractal starts with three circles tangent to each other. A bigger circle is drawn enclosing the three circles and the empty spaces in between are filled with smaller circles tangent to each other. New circles are drawn in the empty spaces and are not allowed to intercect other circles, creating the Apollonian gasket. The curvature of the circles is computed using Descartes' theorem. This collection includes various starting positions and sizes of the three circles, creating variations of the fractal, and everything is randomly coloured. No graphics editor has been used. I hope you derive pleasure and inspiration from Series 9 and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
This is Series 10 of VisualMathArt. The series visualises the Mandelbrot set. The Mandelbrot set is the set of complex numbers f(z)=z^2+c. Each pixel colour visualises whether the iteration diverges to infinity or not. Infinity is marked in black and finite iterations are shown in different colour sets. No graphics editor has been used. I hope you derive pleasure and inspiration from Series 10 and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
This is Series 11 of VisualMathArt. The series visualises the sort algorithms Bubble Sort, Selection Sort, Quick Sort, Insertion Sort, Merge Sort, Heap Sort, Gnome Sort, Radix Sort and Shell Sort. Each image in the sequence represents an iteration step in the sorting algorithm. At the beginning, the numbers with unique colours and gradients in the sequence are randomly distributed and then sorted using the different sorting algorithms. No graphics editor has been used. I hope you derive pleasure and inspiration from Series 11 and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
This is Series 12 of VisualMathArt. The series visualises the Ulam spiral, where the positive integers are drawn in various shapes with or without connections. Note that with some images the prime number is marked or drawn differently, creating a pattern. No graphics editor has been used. I hope you derive pleasure and inspiration from Series 12 and what mathematics can visualise.
Available in High Resolution as a unique Crypto NFT on Polygon OpenSea @VisualMathArt
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Available in High Resolution as a unique Crypto NFT on OpenSea @VisualMathArt
