Compiling and running a program to generate fractal images

• Your chmod needs to go away; d.sh should already have the correct permissions, including when extracted from a source archive
• You should probably delete all of your output diagnostic fluff.
• f.c and d.sh are very bad filenames. The former should probably be renamed to fractal.c or somesuch.
• You've mis-used make. The whole point of make is to express a dependency tree, and to be able to ask for anything in that tree to be generated, in turn generating any missing or out-of-date dependencies on the filesystem. You need to re-think output files (e.g. png) to be make targets, input files (.pgm, .c) to be inputs to recipes, and programs gcc and convert to be the commands within those recipes. Once done, your bash script can go away entirely.
• Don't use a.out. Give your binary a meaningful name.
• A side-effect of the above is that checking like this:

if [ $? -ne 0 ]
then
    echo ERROR: compilation failed !!!!!!
    exit 1
fi

can be deleted; make is smart enough to understand when commands fail.

Re. image filenames such as 1_4000_Fatou_abi_LSCM_zp_cr: you ask

do I have to list manually all the files or can I use wildcards like *.pgm ?

It depends on the desired invocation of your makefile. If you want to start with an empty directory and magically make and have all of your images generate and convert, then you have to manually list all of the file stems in your makefile. If instead you're comfortable with an invocation that looks like

make 1_4000_Fatou_abi_LSCM_zp_cr.png

then you do not have to list out all of your stems. Either you would have your current program just generate all of them (as it would happen now), or (probably better) rework your program so that it accepts a command-line argument and generates a single image on demand. The latter would be much easier to code a meaningful makefile for.

If I were to take a guess, your dependency tree basically looks like this. Beware that it's half untested, and in particular $(IMAGES) will change based on a few factors including whether you know your image file stems.

#!/usr/bin/make -f

export

CFLAGS=-O3 -lm -Wall -march=native -fopenmp --std=c17
OMP_DISPLAY_ENV=FALSE
MAGICK_WIDTH_LIMIT=100MP
MAGICK_HEIGHT_LIMIT=100MP

IMAGES=image1 image2
PGMS=$(IMAGES:=.pgm)
PNGS=$(IMAGES:=.png)


all: $(PNGS)

%.png: %.pgm
    convert $^ -resize 2000x2000 $@

$(PGMS): fractal
    ./$^

fractal: fractal.o
    gcc $$CFLAGS -o $@ $^

%.o: %.c
    gcc $$CFLAGS -o $@ $^ -c

clean:
    rm -f fractal *.o *.pgm *.png

Output:

$ make
gcc $CFLAGS -o fractal.o fractal.c -c
gcc $CFLAGS -o fractal fractal.o
./fractal
convert image1.pgm -resize 2000x2000 image1.png

(convert then fails for me due to it being fed a dummy image but the concept is there.)