.M3F File Format

Introduction

A version 6 formula is a Mandelbulb 3D formula file with .Version = 6. One hundred and ninety of the 714 files examined have it (one hundred and twenty-three different files), and they are mostly the dIFS formulas: MengerIFS, SphereIFS, HeightMapIFS, TorusIFS, transformIFS and many more whose names end in IFS. The program’s readme calls dIFS (distance iterated function system) formulas a type of their own and says some of them need a processor with SSE2. 124 of the version 6 files have .DEoption = 20 and 38 have .DEoption = 21; those values are found in no other version.

Version 6 is also the version with the most options: 2Doubles (119 files), 3SingleAngles (75), 6SingleAngles (18), SingleAngle and ADEscale (24 files) appear here far more than in the others.

The file is Windows text, lines ending in CR LF, and the code is 32-bit x86 written as hexadecimal digits: x87 in some files, SSE2 in the 122 that have a .SSE2 line.

Layout

Option lines

Machine code

Two styles are seen. The x87 files, such as transformIFS, start straight in with fld qword ptr [edi - 0x58] (DD 47 A8) and read their option values at negative offsets from esi and edi, and end with C3 (ret). The SSE2 files, such as SphereIFS, start with movupd xmm0, [esi - 0x78] (66 0F 10 46 88), use packed double instructions (mulpd, addpd) and, in SphereIFS, also end with C3. Neither has the push ebp prologue of the earlier versions, and the registers are set by the program before the call. Some version 6 files still end with C2 08 00. This is read off the disassembly of the sample files.

A worked example

transformIFS.m3f is 487 bytes, with .DEoption = 21, eight option lines and 128 bytes of x87 code.

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 36 0D 0A 2E 44 45 6F 70 74 69   ion = 6  .DEopti
00000020  6F 6E 20 3D 20 32 31 0D 0A 2E 44 6F 75 62 6C 65   on = 21  .Double
00000030  20 41 64 64 20 58 20 3D 20 30 0D 0A 2E 44 6F 75    Add X = 0  .Dou
000000C0  6C 65 20 53 63 61 6C 65 20 3D 20 31 0D 0A 5B 43   le Scale = 1  [C
000000D0  4F 44 45 5D 0D 0A 44 44 34 37 41 38 44 44 34 36 39 38   ODE]  DD47A8DD4698

The options are Add X, Add Y, Add Z (doubles), 3SingleAngles Rotation, Integer Abs X, Abs Y, Abs Z and Double Scale. The code is DD 47 A8 DD 46 98 D8 C9 DC 47 E0 …: fld [edi-0x58], fld [esi-0x68], fmul st, st(1), fadd [edi-0x20] and so on, and it ends DD D8 C3 (fstp st(0); ret).

Quirks

• A byte is never split across two hex lines; the last hex line is shorter.
• An INT64 constant is written with a dollar sign and hexadecimal digits; the explorer shows it as a number too.
• An option kind such as 2Doubles has one line and one default.
• Text in the description may use Windows-1252 characters.

Not described

What this page and the explorer leave out or only infer for version 6 files.

• Reference: what version 6 changes from version 5 is not known; that these are dIFS formulas follows from .DEoption 20 and 21, and only 20 (and the range 20 to 22) has a meaning in the source. The values 6, 2 and 11 seen here are not described.
• Reference: how the SSE2 code receives its data (which registers hold what) and what the INT64 constants are used for are not described; the two styles of code are told from a few examined files.
• Viewer: the machine code is a linear disassembly (no jump following, no data/code separation, constants not shown beside the code); options, including the 2Doubles kind, 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