Formula Atlas

A map of the quadratic family z² + c: choose a point, start at zero, and watch its orbit decide the outcome.

A centered complex logistic map: one parameter both stretches an orbit and turns it back on itself.

A fourth-degree Julia map: raise z to the fourth power, add a fixed c, and four-way branching begins.

A fold-and-scale map inspired by Tom Lowe's 2010 Mandelbox: box reflections, radial folding, and scaling make rooms and walls out of an iteration.

A Perpendicular-family quadratic map: fold the real part before squaring, fold the real result again, and the boundary knots into braids.

A quadratic escape-time fractal: fold both coordinates with absolute values before squaring, and the color bands form an asymmetric ship-like outline.

A Burning Ship relative with an uneven fold: the real part folds directly, while the imaginary part couples signed x to |y|.

Newton's method for z³ − 1: three convergence basins divided by a frontier that never settles down.

Newton's method applied to cosh z = 1: infinitely many evenly spaced roots turn the plane into repeating convergence bands.

A squared Möbius quotient with one pole at z = c, gathering the plane into clustered basins and bead-like chains.

A squared rational map with z² inside the quotient, giving Type 1’s terrain a steeper, more folded form.

A quadratic recurrence with memory: a complex coefficient carries the previous orbit value into the next step, producing feathered, flame-like forms.

A transcendental escape-time map: hyperbolic cosine replaces squaring, and vertically repeating plumes and layered fans take its place.

A rational map that adds c/z to a quadratic orbit; the pole at zero pulls out long legs and web-like filaments.

A folded Burning Ship relative: squared coordinate terms take absolute values, while the cross term keeps x signed and opens broad horns with mirrored inner gates.

A quadratic map that folds both parts of z² + c into the nonnegative quadrant each step, producing double mirror symmetry and compact mandala-like forms.

A degree-2 rational iteration, z²/(z + c), with one zero and a pole that travels as c changes.

A rational map where squaring drives points outward and an inverse-cubic term sends them through the pole at the origin.

A hybrid map that adds a rational quadratic term to the complex logistic recurrence, bringing movable poles into the orbit.

A complex sine map: sine bends the orbit, a fixed 0.55-radian turn rotates it, and c shifts it—an adaptation inspired by George Zaslavsky's 1978 dissipative kicked-rotor map.

A reciprocal quadratic map that swaps near and far at every step: small values fly outward, large ones return toward the origin.