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St. John's, Newfoundland.

Collection

Wallpapers & templates

Mathematical art and templates I’ve made. Browse the previews and follow the Ko-fi link for available downloads.

Browse the collection

An equation becomes a pattern

Julia set — complete mathematical wallpaper

Julia set

Complex numbers, made visible.

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Collection

Wallpapers & templates

Mathematical art and templates I’ve made. Browse the previews and follow the Ko-fi link for available downloads.

Notion Second Brain Template for Productivity, Planning, and Knowledge preview 11 / 2

Notion template

Notion Second Brain Template for Productivity, Planning, and Knowledge

A workspace for notes, tasks, projects and reference material.

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Single-column Overleaf Résumé Template preview 11 / 3

Resume template

Single-column Overleaf Résumé Template

A single-column LaTeX résumé template for Overleaf.

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Lorenz Attractor

Wallpaper

Lorenz Attractor

Chaos theory classic with butterfly-like structure.

x˙=σ(y−x)y˙=x(ρ−z)−yz˙=xy−βz\begin{gathered}\dot{x}=\sigma(y-x) \\ \dot{y}=x(\rho-z)-y \\ \dot{z}=xy-\beta z\end{gathered}
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Barnsley Fern

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Barnsley Fern

Four affine maps sampled with probabilities 0.01, 0.85, 0.07 and 0.07.

f1(x)=[0000.16]xf2(x)=[0.850.04−0.040.85]x+[01.6]f3(x)=[0.2−0.260.230.22]x+[01.6]f4(x)=[−0.150.280.260.24]x+[00.44]\begin{aligned} f_1(\mathbf{x})&=\begin{bmatrix}0&0\\0&0.16\end{bmatrix}\mathbf{x} \\ f_2(\mathbf{x})&=\begin{bmatrix}0.85&0.04\\-0.04&0.85\end{bmatrix}\mathbf{x}+\begin{bmatrix}0\\1.6\end{bmatrix} \\ f_3(\mathbf{x})&=\begin{bmatrix}0.2&-0.26\\0.23&0.22\end{bmatrix}\mathbf{x}+\begin{bmatrix}0\\1.6\end{bmatrix} \\ f_4(\mathbf{x})&=\begin{bmatrix}-0.15&0.28\\0.26&0.24\end{bmatrix}\mathbf{x}+\begin{bmatrix}0\\0.44\end{bmatrix}\end{aligned}
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Clifford Attractor

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Clifford Attractor

Dense, swirling structures from simple recurrences.

xn+1=sin⁡(ayn)+ccos⁡(axn)yn+1=sin⁡(bxn)+dcos⁡(byn)\begin{gathered}x_{n+1}=\sin(a y_n)+c\cos(a x_n) \\ y_{n+1}=\sin(b x_n)+d\cos(b y_n)\end{gathered}
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De Jong Attractor

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De Jong Attractor

Expressive non-linear map with rich textures.

xn+1=sin⁡(ayn)−cos⁡(bxn)yn+1=sin⁡(cxn)−cos⁡(dyn)\begin{gathered}x_{n+1}=\sin(a y_n)-\cos(b x_n) \\ y_{n+1}=\sin(c x_n)-\cos(d y_n)\end{gathered}
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Hénon Map

Wallpaper

Hénon Map

A seminal discrete-time chaotic system.

xn+1=1−axn2+ynyn+1=bxn\begin{gathered}x_{n+1}=1-a x_n^2 + y_n \\ y_{n+1}=b x_n\end{gathered}
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Ikeda Map

Wallpaper

Ikeda Map

An Ikeda map generated with u = 0.9; its angle uses 0.4 − 6/(1 + x² + y²).

t=0.4−61+xn2+yn2xn+1=1+u(xncos⁡t−ynsin⁡t)yn+1=u(xnsin⁡t+yncos⁡t)\begin{gathered}t=0.4-\frac{6}{1+x_n^2+y_n^2} \\ x_{n+1}=1+u(x_n\cos t - y_n\sin t) \\ y_{n+1}=u(x_n\sin t + y_n\cos t)\end{gathered}
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Lissajous Curve

Wallpaper

Lissajous Curve

Two perpendicular sinusoidal oscillations create this curve.

x=Asin⁡(at+δ)y=Bsin⁡(bt)\begin{gathered}x=A\sin(a t+\delta) \\ y=B\sin(b t)\end{gathered}
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Rössler Attractor

Wallpaper

Rössler Attractor

Continuous-time chaos with ribbon-like flow.

x˙=−(y+z)y˙=x+ayz˙=b+z(x−c)\begin{gathered}\dot{x}=-(y+z) \\ \dot{y}=x+a y \\ \dot{z}=b+z(x-c)\end{gathered}
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Aizawa Attractor

Wallpaper

Aizawa Attractor

Aizawa flow with a = 0.95, b = 0.7, c = 0.6, d = 3.5, e = 0.25 and f = 0.1. Colour is an artistic mapping of the trajectory.

x˙=(z−b)x−dyy˙=dx+(z−b)yz˙=c+az−z33−(x2+y2)(1+ez)+fzx3\begin{gathered}\dot{x}=(z-b)x-dy \\ \dot{y}=dx+(z-b)y \\ \dot{z}=c+az-\frac{z^3}{3}-(x^2+y^2)(1+ez)+fzx^3\end{gathered}
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Dadras Attractor

Wallpaper

Dadras Attractor

Electric Dadras attractor with neon lightning effect and dynamic patterns.

x˙=y−ax+byzy˙=cy−xz+zz˙=dxy−ez\begin{gathered}\dot{x}=y-ax+byz \\ \dot{y}=cy-xz+z \\ \dot{z}=dxy-ez\end{gathered}
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Chen Attractor

Wallpaper

Chen Attractor

A quadratic chaotic flow from the collection’s Chen-labelled generator.

x˙=ax−yzy˙=by+xzz˙=cz+xy3\begin{gathered}\dot{x}=ax-yz \\ \dot{y}=by+xz \\ \dot{z}=cz+\frac{xy}{3}\end{gathered}
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Four Wing Attractor

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Four Wing Attractor

Four-winged continuous system creating dramatic lobes.

x˙=ax+yzy˙=bx+cy−xzz˙=−z−xy\begin{gathered}\dot{x}=ax+yz \\ \dot{y}=bx+cy-xz \\ \dot{z}=-z-xy\end{gathered}
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Spirograph

Wallpaper

Spirograph

A hypotrochoid generated with R = 200, r = 80 and tracing distance d = 90.

x=(R−r)cos⁡t+dcos⁡ ⁣(R−rrt)y=(R−r)sin⁡t−dsin⁡ ⁣(R−rrt)\begin{gathered}x=(R-r)\cos t + d\cos\!\left(\tfrac{R-r}{r}t\right) \\ y=(R-r)\sin t - d\sin\!\left(\tfrac{R-r}{r}t\right)\end{gathered}
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Julia Set

Wallpaper

Julia Set

Quadratic iteration with fixed c = −0.7 + 0.27015i and a varying initial z.

zn+1=zn2+cz_{n+1}=z_n^2+c

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Mandelbrot Set

Wallpaper

Mandelbrot Set

Quadratic iteration starting at z = 0, with c varying across the complex plane.

zn+1=zn2+cz_{n+1}=z_n^2+c

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Newton Fractal

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Newton Fractal

Basins of attraction emerging from Newton's method.

zn+1=zn−f(zn)f′(zn) f(z)=z3−1\begin{gathered}z_{n+1}=z_n-\frac{f(z_n)}{f'(z_n)} \\ \ f(z)=z^3-1\end{gathered}

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Tricorn Fractal

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Tricorn Fractal

Conjugate-variant of the quadratic map with threefold symmetry.

zn+1=zn‾2+cz_{n+1}=\overline{z_n}^2+c

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Burning Ship

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Burning Ship

Angular, ship-like silhouette with dramatic ridges.

zn+1=(∣Re⁡(zn)∣+i∣Im⁡(zn)∣)2+cz_{n+1}=(\lvert\operatorname{Re}(z_n)\rvert+i\lvert\operatorname{Im}(z_n)\rvert)^2+c

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Random Math Art

Wallpaper

Random Math Art

Randomly sampled points coloured by trigonometric functions.

x,y∼U(−1,1)x,y\sim\mathcal{U}(-1,1)

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