Mandy

A fractal generator for classic 68k Macintosh computers (since 2016).

What it does

Mandy renders several kinds of image into a window, chosen from the Fractal menu, grouped there by family:

• Tree — a recursive branching tree, drawn directly with QuickDraw lines.
• Barnsley Fern — a fixed iterated-function-system recipe (four affine transformations, applied with fixed probabilities), plotted point by point.
• Sierpinski — Sierpinski's triangle, via the standard three-vertex "chaos game" construction.
• Mandelbrot — the Mandelbrot set.
• Julia — a Julia set at a fixed constant.
• Burning Ship — the Mandelbrot iteration with both of z's parts folded onto the positive axes before squaring, every iteration.
• Tricorn (Mandelbar) — the Mandelbrot iteration against z's complex conjugate.
• Multibrot… — z raised to a chosen power (rather than squared) plus c; opens a dialog to choose the power.
• Phoenix — the Mandelbrot iteration with a memory term feeding back the previous iterate as well as the current one (Ushiki, 1988).
• Lyapunov… — not escape-time at all: colours a driven logistic map by its own Lyapunov exponent (stable vs. chaotic), driven by a sequence of A's and B's entered in a dialog.
• Newton… — Newton's-method convergence toward one of zⁿ − 1's own roots, coloured by which root and how fast; opens a dialog to choose the power (how many roots).

See FractalParameters.md for what each configurable value (marked with "…" in the menu) actually does.

Every sampled fractal type (everything above except Tree, Barnsley Fern, and Sierpinski, which draw directly instead) renders progressively: the image starts at a coarse block size and refines through several passes down to full resolution, with each pass visiting blocks in a recursive quadrant order rather than a plain top-to-bottom scan, so the picture comes into focus as a whole rather than sweeping like a scanline. Rendering happens a little at a time on idle events, so the application stays responsive while a render is in progress. Command-Period aborts a render early, leaving whatever has been drawn so far on screen.

Other features:

• Get Info a small floating window showing the current fractal's resolution, screen depth, render time, and mathematical parameters (zoom, iteration count where meaningful, Julia's constant) - which of these apply varies by fractal type.
• Save As... exports the current image as a PICT file.
• Animate / Stop Animation cycles the displayed colours or patterns without recomputing the fractal. On colour Macs this rotates the image's own colour table.

The application automatically detects whether Color QuickDraw is available and renders in colour where possible, falling back to QuickDraw's standard dither patterns (white/light gray/gray/dark gray/black) on black-and-white screens or at 1-bit/2-bit screen depths.

Requirements

• Classic Mac OS, System 6 or System 7.
• 68k Macintosh hardware. The minimum target is a Mac Plus with 1MB of RAM..
• Works on both black-and-white and colour Macs. Colour Macs need Color QuickDraw.
• The window is a fixed 512×300 — there's no resizing or zoom yet.

Building

MandyWindow is written in classic Mac Toolbox C — plain C against QuickDraw, the Window Manager, and the Menu Manager, not Objective-C, Carbon, or Cocoa. It's built with Think C; no other toolchain has been used or tested against it, though it should port to other 68k Mac Toolbox C environments (MPW, CodeWarrior) without much difficulty.

No third-party libraries are required — only the classic Mac Toolbox headers (Quickdraw.h and friends) and the standard ANSI C library that ships with Think C (<stdio.h>, <math.h>).

Source files

File	Purpose
MandyWindow.c	Application entry point and main event loop
mwWindow.c / .h	Offscreen buffering, window management, progressive-render scheduling, the fractal type registry
mwFractalMath.c / .h	Escape-time iteration, interior/precision shortcuts, pixel-to-plane mapping, log-scaled shading - shared maths with no window or QuickDraw state, reusable for any z^2+c-family fractal
mwLyapunovMath.c / .h	The Lyapunov fractal's own maths - kept separate from mwFractalMath since it isn't escape-time
mwNewtonMath.c / .h	Newton's-method fractal maths - also kept separate, since it's convergence-based rather than escape-time
mwParameterDialog.c / .h	Reusable "enter one or more values" dialog for any fractal type needing runtime configuration (Multibrot's and Newton's power, Lyapunov's driving sequence) - requires a DLOG/DITL resource pair at ID 131, documented at the top of the .c file
mwMenus.c / .h	Menu bar setup and menu command dispatch
mwInfo.c / .h	The Get Info palette window
mwSaveAs.c / .h	Save As... (PICT export) and Save/Load Fractal Data
mwColorCycle.c / .h	The Animate / Stop Animation feature
FractalParameters.md	What each fractal type's own configurable value actually does, for anyone using (or extending) the parameter dialog

Known constraints

A few Toolbox routines were deliberately avoided after testing showed they don't work in this project's build/link setup, in case that trips up future changes:

• SetGWorld reliably crashes on real hardware here — ports are switched with plain SetPort instead.
• PmForeColor and CTabChanged (Palette Manager / Color QuickDraw routines) fail to link — colour is set via direct pixel-memory writes and colour-table manipulation instead of these calls.