.M3F File Format

Introduction

A version 3 formula is a Mandelbulb 3D formula file whose first option line is .Version = 3. Twelve of the 714 files examined have it (six different files, the rest copies): Makin3D-1, Makin3D-2, Makin3D-3-4, GenIntPower, _IntPowRotateC and _AmazingBoxSSE2. The Makin3D files carry David Makin’s name in their description. Four files have a .SSE3 line, a flag found in no other version; two have .SSE2.

The file is Windows text, lines ending in CR LF, and the code is 32-bit x86 written as hexadecimal digits.

Layout

Option lines

Every option line starts with a dot. A setting is read by name; an option, written .<kind> <label> = <default>, is a value the user can change.

No version 3 file has a 2Doubles, an angle, or a Single option.

Machine code

As in the other versions the code is a procedure: it starts 55 8B EC (push ebp; mov ebp, esp), loads [ebp+8], takes the pointer at offset 0x30 of what that points to for its option values, and works on x, y and z through eax, edx and ecx (in Makin3D-1 it copies eax to ebx first and ends with mov eax, ebx). The code of Makin3D-1 has D9 D0, an x87 fnop, between its steps. Most of the twelve files end with C2 08 00 (ret 8), some with a plain C3. This is read off the disassembly of the sample files.

A worked example

Makin3D-1.m3f is 409 bytes. Its description says it comes from David Makin’s MMFwip3D.ufm, and gives x' = x*x - y*y - z*z + Cx. It has no .DEoption.

00000000  5B 4F 50 54 49 4F 4E 53 5D 0D 0A 2E 56 65 72 73   [OPTIONS]  .Vers
00000010  69 6F 6E 20 3D 20 33 0D 0A 2E 44 45 73 63 61 6C   ion = 3  .DEscal
00000020  65 20 3D 20 31 0D 0A 2E 53 49 70 6F 77 65 72 20   e = 1  .SIpower 
00000030  3D 20 32 0D 0A 5B 43 4F 44 45 5D 0D 0A 35 35 38   = 2  [CODE]  558
00000040  42 45 43 35 33 35 36 35 37 38 42 37 35 30 38 38   BEC5356578B75088

The code begins 55 8B EC 53 56 57 8B 75 08 8B 7E 30 8B D8 DD 03 D8 C8: push ebp; mov ebp, esp; push ebx; push esi; push edi; mov esi,[ebp+8]; mov edi,[esi+0x30]; mov ebx, eax; fld qword ptr [ebx]; fmul st, st(0), which starts squaring x.

Quirks

• A byte is never split across two hex lines; the last hex line is shorter.
• The description starts after a blank line; Makin3D-1 has two blank lines after [END].
• Text in the description may use Windows-1252 characters.

Not described

What this page and the explorer leave out or only infer for version 3 files.

• Reference: only six different files (twelve with copies) have this version, so what is said of it may not hold for others; what the number changes from version 2 is not known.
• Reference: the .DEoption values 0 and 11 seen here have no stated meaning in the source; the SSE2 and SSE3 flags are described from the loader, not from what the code does with them; the code’s register use is read off the disassembly of sample files.
• Viewer: the machine code is a linear disassembly (no jump following, no data/code separation, constants not shown beside the code); options are not linked to the code that reads them.

Variants

• Version 2 – the commonest: x87 code with a push ebp prologue, many add-ons
• Version 3 – twelve files, among them David Makin’s formulas, with SSE2 and SSE3 flags
• Version 4 – twenty-eight files, the reciprocal add-ons and Amazing Box variants
• Version 5 – sixty-one files, mostly four-dimensional formulas
• Version 6 – one hundred and ninety files, mostly the dIFS formulas
• Version 8 – six files, the newest number seen

Links